CINXE.COM

(PDF) Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics

<!DOCTYPE html> <html > <head> <meta charset="utf-8"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <meta content="width=device-width, initial-scale=1" name="viewport"> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs"> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="y8KEMyhg8U1Sl5DDXQ7PEkj3uGi6VHgQvi01F_iWg519MxED53hZWBgcGaaVIDDjPjo62wjM_41kKqgAKFfXWg" /> <meta name="citation_title" content="Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics" /> <meta name="citation_journal_title" content="cs.qub.ac.uk" /> <meta name="citation_author" content="Zhi-hui Luo" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:url" content="https://www.academia.edu/974166/Knowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics" /> <meta name="twitter:title" content="Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics" /> <meta name="twitter:description" content="Academia.edu is a platform for academics to share research papers." /> <meta name="twitter:image" content="http://a.academia-assets.com/images/twitter-card.jpeg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/974166/Knowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics" /> <meta property="og:title" content="Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics" /> <meta property="article:author" content="https://columbia.academia.edu/ZhihuiLuo" /> <meta name="description" content="Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics" /> <title>(PDF) Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics</title> <link rel="canonical" href="https://www.academia.edu/974166/Knowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '5e761fc7f2723937bfa23c00d57d97019322a224'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1740636896000); window.Aedu.timeDifference = new Date().getTime() - 1740636896000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","author":[{"@context":"https://schema.org","@type":"Person","name":"Zhi-hui Luo","url":"https://columbia.academia.edu/ZhihuiLuo"}],"contributor":[],"dateCreated":"2011-10-03","headline":"Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics","image":"https://attachments.academia-assets.com/5958495/thumbnails/1.jpg","inLanguage":"en","keywords":[],"publication":"cs.qub.ac.uk","publisher":{"@context":"https://schema.org","@type":"Organization","name":null},"sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":"columbia"}],"thumbnailUrl":"https://attachments.academia-assets.com/5958495/thumbnails/1.jpg","url":"https://www.academia.edu/974166/Knowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics"}</script><style type="text/css">@media(max-width: 567px){:root{--token-mode: Rebrand;--dropshadow: 0 2px 4px 0 #22223340;--primary-brand: #0645b1;--error-dark: #b60000;--success-dark: #05b01c;--inactive-fill: #ebebee;--hover: #0c3b8d;--pressed: #082f75;--button-primary-fill-inactive: #ebebee;--button-primary-fill: #0645b1;--button-primary-text: #ffffff;--button-primary-fill-hover: #0c3b8d;--button-primary-fill-press: #082f75;--button-primary-icon: #ffffff;--button-primary-fill-inverse: #ffffff;--button-primary-text-inverse: #082f75;--button-primary-icon-inverse: #0645b1;--button-primary-fill-inverse-hover: #cddaef;--button-primary-stroke-inverse-pressed: #0645b1;--button-secondary-stroke-inactive: #b1b1ba;--button-secondary-fill: #eef2f9;--button-secondary-text: #082f75;--button-secondary-fill-press: #cddaef;--button-secondary-fill-inactive: #ebebee;--button-secondary-stroke: #cddaef;--button-secondary-stroke-hover: #386ac1;--button-secondary-stroke-press: #0645b1;--button-secondary-text-inactive: #b1b1ba;--button-secondary-icon: #082f75;--button-secondary-fill-hover: #e6ecf7;--button-secondary-stroke-inverse: #ffffff;--button-secondary-fill-inverse: rgba(255, 255, 255, 0);--button-secondary-icon-inverse: #ffffff;--button-secondary-icon-hover: #082f75;--button-secondary-icon-press: #082f75;--button-secondary-text-inverse: #ffffff;--button-secondary-text-hover: #082f75;--button-secondary-text-press: #082f75;--button-secondary-fill-inverse-hover: #043059;--button-xs-stroke: #141413;--button-xs-stroke-hover: #0c3b8d;--button-xs-stroke-press: #082f75;--button-xs-stroke-inactive: #ebebee;--button-xs-text: #141413;--button-xs-text-hover: #0c3b8d;--button-xs-text-press: #082f75;--button-xs-text-inactive: #91919e;--button-xs-icon: #141413;--button-xs-icon-hover: #0c3b8d;--button-xs-icon-press: #082f75;--button-xs-icon-inactive: #91919e;--button-xs-fill: #ffffff;--button-xs-fill-hover: #f4f7fc;--button-xs-fill-press: #eef2f9;--buttons-button-text-inactive: #91919e;--buttons-button-focus: #0645b1;--buttons-button-icon-inactive: #91919e;--buttons-small-buttons-corner-radius: 16px;--buttons-small-buttons-l-r-padding: 20px;--buttons-small-buttons-height: 48px;--buttons-small-buttons-gap: 8px;--buttons-small-buttons-icon-only-width: 48px;--buttons-small-buttons-icon-size: 20px;--buttons-small-buttons-stroke-default: 1px;--buttons-small-buttons-stroke-thick: 2px;--buttons-large-buttons-l-r-padding: 32px;--buttons-large-buttons-height: 64px;--buttons-large-buttons-icon-only-width: 64px;--buttons-large-buttons-icon-size: 20px;--buttons-large-buttons-gap: 8px;--buttons-large-buttons-corner-radius: 16px;--buttons-large-buttons-stroke-default: 1px;--buttons-large-buttons-stroke-thick: 2px;--buttons-extra-small-buttons-l-r-padding: 8px;--buttons-extra-small-buttons-height: 32px;--buttons-extra-small-buttons-icon-size: 16px;--buttons-extra-small-buttons-gap: 4px;--buttons-extra-small-buttons-corner-radius: 8px;--buttons-stroke-default: 1px;--buttons-stroke-thick: 2px;--background-beige: #f9f7f4;--error-light: #fff2f2;--text-placeholder: #6d6d7d;--stroke-dark: #141413;--stroke-light: #dddde2;--stroke-medium: #535366;--accent-green: #ccffd4;--accent-turquoise: #ccf7ff;--accent-yellow: #f7ffcc;--accent-peach: #ffd4cc;--accent-violet: #f7ccff;--accent-purple: #f4f7fc;--text-primary: #141413;--secondary-brand: #141413;--text-hover: #0c3b8d;--text-white: #ffffff;--text-link: #0645b1;--text-press: #082f75;--success-light: #f0f8f1;--background-light-blue: #f4f7fc;--background-white: #ffffff;--premium-dark: #877440;--premium-light: #f9f6ed;--stroke-white: #ffffff;--inactive-content: #b1b1ba;--annotate-light: #a35dff;--annotate-dark: #824acc;--grid: #eef2f9;--inactive-stroke: #ebebee;--shadow: rgba(34, 34, 51, 0.25);--text-inactive: #6d6d7d;--text-error: #b60000;--stroke-error: #b60000;--background-error: #fff2f2;--background-black: #141413;--icon-default: #141413;--icon-blue: #0645b1;--background-grey: #dddde2;--icon-grey: #b1b1ba;--text-focus: #082f75;--brand-colors-neutral-black: #141413;--brand-colors-neutral-900: #535366;--brand-colors-neutral-800: #6d6d7d;--brand-colors-neutral-700: #91919e;--brand-colors-neutral-600: #b1b1ba;--brand-colors-neutral-500: #c8c8cf;--brand-colors-neutral-400: #dddde2;--brand-colors-neutral-300: #ebebee;--brand-colors-neutral-200: #f8f8fb;--brand-colors-neutral-100: #fafafa;--brand-colors-neutral-white: #ffffff;--brand-colors-blue-900: #043059;--brand-colors-blue-800: #082f75;--brand-colors-blue-700: #0c3b8d;--brand-colors-blue-600: #0645b1;--brand-colors-blue-500: #386ac1;--brand-colors-blue-400: #cddaef;--brand-colors-blue-300: #e6ecf7;--brand-colors-blue-200: #eef2f9;--brand-colors-blue-100: #f4f7fc;--brand-colors-gold-500: #877440;--brand-colors-gold-400: #e9e3d4;--brand-colors-gold-300: #f2efe8;--brand-colors-gold-200: #f9f6ed;--brand-colors-gold-100: #f9f7f4;--brand-colors-error-900: #920000;--brand-colors-error-500: #b60000;--brand-colors-success-900: #035c0f;--brand-colors-green: #ccffd4;--brand-colors-turquoise: #ccf7ff;--brand-colors-yellow: #f7ffcc;--brand-colors-peach: #ffd4cc;--brand-colors-violet: #f7ccff;--brand-colors-error-100: #fff2f2;--brand-colors-success-500: #05b01c;--brand-colors-success-100: #f0f8f1;--text-secondary: #535366;--icon-white: #ffffff;--background-beige-darker: #f2efe8;--icon-dark-grey: #535366;--type-font-family-sans-serif: DM Sans;--type-font-family-serif: Gupter;--type-font-family-mono: IBM Plex Mono;--type-weights-300: 300;--type-weights-400: 400;--type-weights-500: 500;--type-weights-700: 700;--type-sizes-12: 12px;--type-sizes-14: 14px;--type-sizes-16: 16px;--type-sizes-18: 18px;--type-sizes-20: 20px;--type-sizes-22: 22px;--type-sizes-24: 24px;--type-sizes-28: 28px;--type-sizes-30: 30px;--type-sizes-32: 32px;--type-sizes-40: 40px;--type-sizes-42: 42px;--type-sizes-48-2: 48px;--type-line-heights-16: 16px;--type-line-heights-20: 20px;--type-line-heights-23: 23px;--type-line-heights-24: 24px;--type-line-heights-25: 25px;--type-line-heights-26: 26px;--type-line-heights-29: 29px;--type-line-heights-30: 30px;--type-line-heights-32: 32px;--type-line-heights-34: 34px;--type-line-heights-35: 35px;--type-line-heights-36: 36px;--type-line-heights-38: 38px;--type-line-heights-40: 40px;--type-line-heights-46: 46px;--type-line-heights-48: 48px;--type-line-heights-52: 52px;--type-line-heights-58: 58px;--type-line-heights-68: 68px;--type-line-heights-74: 74px;--type-line-heights-82: 82px;--type-paragraph-spacings-0: 0px;--type-paragraph-spacings-4: 4px;--type-paragraph-spacings-8: 8px;--type-paragraph-spacings-16: 16px;--type-sans-serif-xl-font-weight: 400;--type-sans-serif-xl-size: 32px;--type-sans-serif-xl-line-height: 46px;--type-sans-serif-xl-paragraph-spacing: 16px;--type-sans-serif-lg-font-weight: 400;--type-sans-serif-lg-size: 30px;--type-sans-serif-lg-line-height: 36px;--type-sans-serif-lg-paragraph-spacing: 16px;--type-sans-serif-md-font-weight: 400;--type-sans-serif-md-line-height: 30px;--type-sans-serif-md-paragraph-spacing: 16px;--type-sans-serif-md-size: 24px;--type-sans-serif-xs-font-weight: 700;--type-sans-serif-xs-line-height: 24px;--type-sans-serif-xs-paragraph-spacing: 0px;--type-sans-serif-xs-size: 18px;--type-sans-serif-sm-font-weight: 400;--type-sans-serif-sm-line-height: 32px;--type-sans-serif-sm-paragraph-spacing: 16px;--type-sans-serif-sm-size: 20px;--type-body-xl-font-weight: 400;--type-body-xl-size: 24px;--type-body-xl-line-height: 36px;--type-body-xl-paragraph-spacing: 0px;--type-body-sm-font-weight: 400;--type-body-sm-size: 14px;--type-body-sm-line-height: 20px;--type-body-sm-paragraph-spacing: 8px;--type-body-xs-font-weight: 400;--type-body-xs-size: 12px;--type-body-xs-line-height: 16px;--type-body-xs-paragraph-spacing: 0px;--type-body-md-font-weight: 400;--type-body-md-size: 16px;--type-body-md-line-height: 20px;--type-body-md-paragraph-spacing: 4px;--type-body-lg-font-weight: 400;--type-body-lg-size: 20px;--type-body-lg-line-height: 26px;--type-body-lg-paragraph-spacing: 16px;--type-body-lg-medium-font-weight: 500;--type-body-lg-medium-size: 20px;--type-body-lg-medium-line-height: 32px;--type-body-lg-medium-paragraph-spacing: 16px;--type-body-md-medium-font-weight: 500;--type-body-md-medium-size: 16px;--type-body-md-medium-line-height: 20px;--type-body-md-medium-paragraph-spacing: 4px;--type-body-sm-bold-font-weight: 700;--type-body-sm-bold-size: 14px;--type-body-sm-bold-line-height: 20px;--type-body-sm-bold-paragraph-spacing: 8px;--type-body-sm-medium-font-weight: 500;--type-body-sm-medium-size: 14px;--type-body-sm-medium-line-height: 20px;--type-body-sm-medium-paragraph-spacing: 8px;--type-serif-md-font-weight: 400;--type-serif-md-size: 32px;--type-serif-md-paragraph-spacing: 0px;--type-serif-md-line-height: 40px;--type-serif-sm-font-weight: 400;--type-serif-sm-size: 24px;--type-serif-sm-paragraph-spacing: 0px;--type-serif-sm-line-height: 26px;--type-serif-lg-font-weight: 400;--type-serif-lg-size: 48px;--type-serif-lg-paragraph-spacing: 0px;--type-serif-lg-line-height: 52px;--type-serif-xs-font-weight: 400;--type-serif-xs-size: 18px;--type-serif-xs-line-height: 24px;--type-serif-xs-paragraph-spacing: 0px;--type-serif-xl-font-weight: 400;--type-serif-xl-size: 48px;--type-serif-xl-paragraph-spacing: 0px;--type-serif-xl-line-height: 58px;--type-mono-md-font-weight: 400;--type-mono-md-size: 22px;--type-mono-md-line-height: 24px;--type-mono-md-paragraph-spacing: 0px;--type-mono-lg-font-weight: 400;--type-mono-lg-size: 40px;--type-mono-lg-line-height: 40px;--type-mono-lg-paragraph-spacing: 0px;--type-mono-sm-font-weight: 400;--type-mono-sm-size: 14px;--type-mono-sm-line-height: 24px;--type-mono-sm-paragraph-spacing: 0px;--spacing-xs-4: 4px;--spacing-xs-8: 8px;--spacing-xs-16: 16px;--spacing-sm-24: 24px;--spacing-sm-32: 32px;--spacing-md-40: 40px;--spacing-md-48: 48px;--spacing-lg-64: 64px;--spacing-lg-80: 80px;--spacing-xlg-104: 104px;--spacing-xlg-152: 152px;--spacing-xs-12: 12px;--spacing-page-section: 80px;--spacing-card-list-spacing: 48px;--spacing-text-section-spacing: 64px;--spacing-md-xs-headings: 40px;--corner-radius-radius-lg: 16px;--corner-radius-radius-sm: 4px;--corner-radius-radius-md: 8px;--corner-radius-radius-round: 104px}}@media(min-width: 568px)and (max-width: 1279px){:root{--token-mode: Rebrand;--dropshadow: 0 2px 4px 0 #22223340;--primary-brand: #0645b1;--error-dark: #b60000;--success-dark: #05b01c;--inactive-fill: #ebebee;--hover: #0c3b8d;--pressed: #082f75;--button-primary-fill-inactive: #ebebee;--button-primary-fill: #0645b1;--button-primary-text: #ffffff;--button-primary-fill-hover: #0c3b8d;--button-primary-fill-press: #082f75;--button-primary-icon: #ffffff;--button-primary-fill-inverse: #ffffff;--button-primary-text-inverse: #082f75;--button-primary-icon-inverse: #0645b1;--button-primary-fill-inverse-hover: #cddaef;--button-primary-stroke-inverse-pressed: #0645b1;--button-secondary-stroke-inactive: #b1b1ba;--button-secondary-fill: #eef2f9;--button-secondary-text: #082f75;--button-secondary-fill-press: #cddaef;--button-secondary-fill-inactive: #ebebee;--button-secondary-stroke: #cddaef;--button-secondary-stroke-hover: #386ac1;--button-secondary-stroke-press: #0645b1;--button-secondary-text-inactive: #b1b1ba;--button-secondary-icon: #082f75;--button-secondary-fill-hover: #e6ecf7;--button-secondary-stroke-inverse: #ffffff;--button-secondary-fill-inverse: rgba(255, 255, 255, 0);--button-secondary-icon-inverse: #ffffff;--button-secondary-icon-hover: #082f75;--button-secondary-icon-press: #082f75;--button-secondary-text-inverse: #ffffff;--button-secondary-text-hover: #082f75;--button-secondary-text-press: #082f75;--button-secondary-fill-inverse-hover: #043059;--button-xs-stroke: #141413;--button-xs-stroke-hover: #0c3b8d;--button-xs-stroke-press: #082f75;--button-xs-stroke-inactive: #ebebee;--button-xs-text: #141413;--button-xs-text-hover: #0c3b8d;--button-xs-text-press: #082f75;--button-xs-text-inactive: #91919e;--button-xs-icon: #141413;--button-xs-icon-hover: #0c3b8d;--button-xs-icon-press: #082f75;--button-xs-icon-inactive: #91919e;--button-xs-fill: #ffffff;--button-xs-fill-hover: #f4f7fc;--button-xs-fill-press: #eef2f9;--buttons-button-text-inactive: #91919e;--buttons-button-focus: #0645b1;--buttons-button-icon-inactive: #91919e;--buttons-small-buttons-corner-radius: 16px;--buttons-small-buttons-l-r-padding: 20px;--buttons-small-buttons-height: 48px;--buttons-small-buttons-gap: 8px;--buttons-small-buttons-icon-only-width: 48px;--buttons-small-buttons-icon-size: 20px;--buttons-small-buttons-stroke-default: 1px;--buttons-small-buttons-stroke-thick: 2px;--buttons-large-buttons-l-r-padding: 32px;--buttons-large-buttons-height: 64px;--buttons-large-buttons-icon-only-width: 64px;--buttons-large-buttons-icon-size: 20px;--buttons-large-buttons-gap: 8px;--buttons-large-buttons-corner-radius: 16px;--buttons-large-buttons-stroke-default: 1px;--buttons-large-buttons-stroke-thick: 2px;--buttons-extra-small-buttons-l-r-padding: 8px;--buttons-extra-small-buttons-height: 32px;--buttons-extra-small-buttons-icon-size: 16px;--buttons-extra-small-buttons-gap: 4px;--buttons-extra-small-buttons-corner-radius: 8px;--buttons-stroke-default: 1px;--buttons-stroke-thick: 2px;--background-beige: #f9f7f4;--error-light: #fff2f2;--text-placeholder: #6d6d7d;--stroke-dark: #141413;--stroke-light: #dddde2;--stroke-medium: #535366;--accent-green: #ccffd4;--accent-turquoise: #ccf7ff;--accent-yellow: #f7ffcc;--accent-peach: #ffd4cc;--accent-violet: #f7ccff;--accent-purple: #f4f7fc;--text-primary: #141413;--secondary-brand: #141413;--text-hover: #0c3b8d;--text-white: #ffffff;--text-link: #0645b1;--text-press: #082f75;--success-light: #f0f8f1;--background-light-blue: #f4f7fc;--background-white: #ffffff;--premium-dark: #877440;--premium-light: #f9f6ed;--stroke-white: #ffffff;--inactive-content: #b1b1ba;--annotate-light: #a35dff;--annotate-dark: #824acc;--grid: #eef2f9;--inactive-stroke: #ebebee;--shadow: rgba(34, 34, 51, 0.25);--text-inactive: #6d6d7d;--text-error: #b60000;--stroke-error: #b60000;--background-error: #fff2f2;--background-black: #141413;--icon-default: #141413;--icon-blue: #0645b1;--background-grey: #dddde2;--icon-grey: #b1b1ba;--text-focus: #082f75;--brand-colors-neutral-black: #141413;--brand-colors-neutral-900: #535366;--brand-colors-neutral-800: #6d6d7d;--brand-colors-neutral-700: #91919e;--brand-colors-neutral-600: #b1b1ba;--brand-colors-neutral-500: #c8c8cf;--brand-colors-neutral-400: #dddde2;--brand-colors-neutral-300: #ebebee;--brand-colors-neutral-200: #f8f8fb;--brand-colors-neutral-100: #fafafa;--brand-colors-neutral-white: #ffffff;--brand-colors-blue-900: #043059;--brand-colors-blue-800: #082f75;--brand-colors-blue-700: #0c3b8d;--brand-colors-blue-600: #0645b1;--brand-colors-blue-500: #386ac1;--brand-colors-blue-400: #cddaef;--brand-colors-blue-300: #e6ecf7;--brand-colors-blue-200: #eef2f9;--brand-colors-blue-100: #f4f7fc;--brand-colors-gold-500: #877440;--brand-colors-gold-400: #e9e3d4;--brand-colors-gold-300: #f2efe8;--brand-colors-gold-200: #f9f6ed;--brand-colors-gold-100: #f9f7f4;--brand-colors-error-900: #920000;--brand-colors-error-500: #b60000;--brand-colors-success-900: #035c0f;--brand-colors-green: #ccffd4;--brand-colors-turquoise: #ccf7ff;--brand-colors-yellow: #f7ffcc;--brand-colors-peach: #ffd4cc;--brand-colors-violet: #f7ccff;--brand-colors-error-100: #fff2f2;--brand-colors-success-500: #05b01c;--brand-colors-success-100: #f0f8f1;--text-secondary: #535366;--icon-white: #ffffff;--background-beige-darker: #f2efe8;--icon-dark-grey: #535366;--type-font-family-sans-serif: DM Sans;--type-font-family-serif: Gupter;--type-font-family-mono: IBM Plex Mono;--type-weights-300: 300;--type-weights-400: 400;--type-weights-500: 500;--type-weights-700: 700;--type-sizes-12: 12px;--type-sizes-14: 14px;--type-sizes-16: 16px;--type-sizes-18: 18px;--type-sizes-20: 20px;--type-sizes-22: 22px;--type-sizes-24: 24px;--type-sizes-28: 28px;--type-sizes-30: 30px;--type-sizes-32: 32px;--type-sizes-40: 40px;--type-sizes-42: 42px;--type-sizes-48-2: 48px;--type-line-heights-16: 16px;--type-line-heights-20: 20px;--type-line-heights-23: 23px;--type-line-heights-24: 24px;--type-line-heights-25: 25px;--type-line-heights-26: 26px;--type-line-heights-29: 29px;--type-line-heights-30: 30px;--type-line-heights-32: 32px;--type-line-heights-34: 34px;--type-line-heights-35: 35px;--type-line-heights-36: 36px;--type-line-heights-38: 38px;--type-line-heights-40: 40px;--type-line-heights-46: 46px;--type-line-heights-48: 48px;--type-line-heights-52: 52px;--type-line-heights-58: 58px;--type-line-heights-68: 68px;--type-line-heights-74: 74px;--type-line-heights-82: 82px;--type-paragraph-spacings-0: 0px;--type-paragraph-spacings-4: 4px;--type-paragraph-spacings-8: 8px;--type-paragraph-spacings-16: 16px;--type-sans-serif-xl-font-weight: 400;--type-sans-serif-xl-size: 42px;--type-sans-serif-xl-line-height: 46px;--type-sans-serif-xl-paragraph-spacing: 16px;--type-sans-serif-lg-font-weight: 400;--type-sans-serif-lg-size: 32px;--type-sans-serif-lg-line-height: 36px;--type-sans-serif-lg-paragraph-spacing: 16px;--type-sans-serif-md-font-weight: 400;--type-sans-serif-md-line-height: 34px;--type-sans-serif-md-paragraph-spacing: 16px;--type-sans-serif-md-size: 28px;--type-sans-serif-xs-font-weight: 700;--type-sans-serif-xs-line-height: 25px;--type-sans-serif-xs-paragraph-spacing: 0px;--type-sans-serif-xs-size: 20px;--type-sans-serif-sm-font-weight: 400;--type-sans-serif-sm-line-height: 30px;--type-sans-serif-sm-paragraph-spacing: 16px;--type-sans-serif-sm-size: 24px;--type-body-xl-font-weight: 400;--type-body-xl-size: 24px;--type-body-xl-line-height: 36px;--type-body-xl-paragraph-spacing: 0px;--type-body-sm-font-weight: 400;--type-body-sm-size: 14px;--type-body-sm-line-height: 20px;--type-body-sm-paragraph-spacing: 8px;--type-body-xs-font-weight: 400;--type-body-xs-size: 12px;--type-body-xs-line-height: 16px;--type-body-xs-paragraph-spacing: 0px;--type-body-md-font-weight: 400;--type-body-md-size: 16px;--type-body-md-line-height: 20px;--type-body-md-paragraph-spacing: 4px;--type-body-lg-font-weight: 400;--type-body-lg-size: 20px;--type-body-lg-line-height: 26px;--type-body-lg-paragraph-spacing: 16px;--type-body-lg-medium-font-weight: 500;--type-body-lg-medium-size: 20px;--type-body-lg-medium-line-height: 32px;--type-body-lg-medium-paragraph-spacing: 16px;--type-body-md-medium-font-weight: 500;--type-body-md-medium-size: 16px;--type-body-md-medium-line-height: 20px;--type-body-md-medium-paragraph-spacing: 4px;--type-body-sm-bold-font-weight: 700;--type-body-sm-bold-size: 14px;--type-body-sm-bold-line-height: 20px;--type-body-sm-bold-paragraph-spacing: 8px;--type-body-sm-medium-font-weight: 500;--type-body-sm-medium-size: 14px;--type-body-sm-medium-line-height: 20px;--type-body-sm-medium-paragraph-spacing: 8px;--type-serif-md-font-weight: 400;--type-serif-md-size: 40px;--type-serif-md-paragraph-spacing: 0px;--type-serif-md-line-height: 48px;--type-serif-sm-font-weight: 400;--type-serif-sm-size: 28px;--type-serif-sm-paragraph-spacing: 0px;--type-serif-sm-line-height: 32px;--type-serif-lg-font-weight: 400;--type-serif-lg-size: 58px;--type-serif-lg-paragraph-spacing: 0px;--type-serif-lg-line-height: 68px;--type-serif-xs-font-weight: 400;--type-serif-xs-size: 18px;--type-serif-xs-line-height: 24px;--type-serif-xs-paragraph-spacing: 0px;--type-serif-xl-font-weight: 400;--type-serif-xl-size: 74px;--type-serif-xl-paragraph-spacing: 0px;--type-serif-xl-line-height: 82px;--type-mono-md-font-weight: 400;--type-mono-md-size: 22px;--type-mono-md-line-height: 24px;--type-mono-md-paragraph-spacing: 0px;--type-mono-lg-font-weight: 400;--type-mono-lg-size: 40px;--type-mono-lg-line-height: 40px;--type-mono-lg-paragraph-spacing: 0px;--type-mono-sm-font-weight: 400;--type-mono-sm-size: 14px;--type-mono-sm-line-height: 24px;--type-mono-sm-paragraph-spacing: 0px;--spacing-xs-4: 4px;--spacing-xs-8: 8px;--spacing-xs-16: 16px;--spacing-sm-24: 24px;--spacing-sm-32: 32px;--spacing-md-40: 40px;--spacing-md-48: 48px;--spacing-lg-64: 64px;--spacing-lg-80: 80px;--spacing-xlg-104: 104px;--spacing-xlg-152: 152px;--spacing-xs-12: 12px;--spacing-page-section: 104px;--spacing-card-list-spacing: 48px;--spacing-text-section-spacing: 80px;--spacing-md-xs-headings: 40px;--corner-radius-radius-lg: 16px;--corner-radius-radius-sm: 4px;--corner-radius-radius-md: 8px;--corner-radius-radius-round: 104px}}@media(min-width: 1280px){:root{--token-mode: Rebrand;--dropshadow: 0 2px 4px 0 #22223340;--primary-brand: #0645b1;--error-dark: #b60000;--success-dark: #05b01c;--inactive-fill: #ebebee;--hover: #0c3b8d;--pressed: #082f75;--button-primary-fill-inactive: #ebebee;--button-primary-fill: #0645b1;--button-primary-text: #ffffff;--button-primary-fill-hover: #0c3b8d;--button-primary-fill-press: #082f75;--button-primary-icon: #ffffff;--button-primary-fill-inverse: #ffffff;--button-primary-text-inverse: #082f75;--button-primary-icon-inverse: #0645b1;--button-primary-fill-inverse-hover: #cddaef;--button-primary-stroke-inverse-pressed: #0645b1;--button-secondary-stroke-inactive: #b1b1ba;--button-secondary-fill: #eef2f9;--button-secondary-text: #082f75;--button-secondary-fill-press: #cddaef;--button-secondary-fill-inactive: #ebebee;--button-secondary-stroke: #cddaef;--button-secondary-stroke-hover: #386ac1;--button-secondary-stroke-press: #0645b1;--button-secondary-text-inactive: #b1b1ba;--button-secondary-icon: #082f75;--button-secondary-fill-hover: #e6ecf7;--button-secondary-stroke-inverse: #ffffff;--button-secondary-fill-inverse: rgba(255, 255, 255, 0);--button-secondary-icon-inverse: #ffffff;--button-secondary-icon-hover: #082f75;--button-secondary-icon-press: #082f75;--button-secondary-text-inverse: #ffffff;--button-secondary-text-hover: #082f75;--button-secondary-text-press: #082f75;--button-secondary-fill-inverse-hover: #043059;--button-xs-stroke: #141413;--button-xs-stroke-hover: #0c3b8d;--button-xs-stroke-press: #082f75;--button-xs-stroke-inactive: #ebebee;--button-xs-text: #141413;--button-xs-text-hover: #0c3b8d;--button-xs-text-press: #082f75;--button-xs-text-inactive: #91919e;--button-xs-icon: #141413;--button-xs-icon-hover: #0c3b8d;--button-xs-icon-press: #082f75;--button-xs-icon-inactive: #91919e;--button-xs-fill: #ffffff;--button-xs-fill-hover: #f4f7fc;--button-xs-fill-press: #eef2f9;--buttons-button-text-inactive: #91919e;--buttons-button-focus: #0645b1;--buttons-button-icon-inactive: #91919e;--buttons-small-buttons-corner-radius: 16px;--buttons-small-buttons-l-r-padding: 20px;--buttons-small-buttons-height: 48px;--buttons-small-buttons-gap: 8px;--buttons-small-buttons-icon-only-width: 48px;--buttons-small-buttons-icon-size: 20px;--buttons-small-buttons-stroke-default: 1px;--buttons-small-buttons-stroke-thick: 2px;--buttons-large-buttons-l-r-padding: 32px;--buttons-large-buttons-height: 64px;--buttons-large-buttons-icon-only-width: 64px;--buttons-large-buttons-icon-size: 20px;--buttons-large-buttons-gap: 8px;--buttons-large-buttons-corner-radius: 16px;--buttons-large-buttons-stroke-default: 1px;--buttons-large-buttons-stroke-thick: 2px;--buttons-extra-small-buttons-l-r-padding: 8px;--buttons-extra-small-buttons-height: 32px;--buttons-extra-small-buttons-icon-size: 16px;--buttons-extra-small-buttons-gap: 4px;--buttons-extra-small-buttons-corner-radius: 8px;--buttons-stroke-default: 1px;--buttons-stroke-thick: 2px;--background-beige: #f9f7f4;--error-light: #fff2f2;--text-placeholder: #6d6d7d;--stroke-dark: #141413;--stroke-light: #dddde2;--stroke-medium: #535366;--accent-green: #ccffd4;--accent-turquoise: #ccf7ff;--accent-yellow: #f7ffcc;--accent-peach: #ffd4cc;--accent-violet: #f7ccff;--accent-purple: #f4f7fc;--text-primary: #141413;--secondary-brand: #141413;--text-hover: #0c3b8d;--text-white: #ffffff;--text-link: #0645b1;--text-press: #082f75;--success-light: #f0f8f1;--background-light-blue: #f4f7fc;--background-white: #ffffff;--premium-dark: #877440;--premium-light: #f9f6ed;--stroke-white: #ffffff;--inactive-content: #b1b1ba;--annotate-light: #a35dff;--annotate-dark: #824acc;--grid: #eef2f9;--inactive-stroke: #ebebee;--shadow: rgba(34, 34, 51, 0.25);--text-inactive: #6d6d7d;--text-error: #b60000;--stroke-error: #b60000;--background-error: #fff2f2;--background-black: #141413;--icon-default: #141413;--icon-blue: #0645b1;--background-grey: #dddde2;--icon-grey: #b1b1ba;--text-focus: #082f75;--brand-colors-neutral-black: #141413;--brand-colors-neutral-900: #535366;--brand-colors-neutral-800: #6d6d7d;--brand-colors-neutral-700: #91919e;--brand-colors-neutral-600: #b1b1ba;--brand-colors-neutral-500: #c8c8cf;--brand-colors-neutral-400: #dddde2;--brand-colors-neutral-300: #ebebee;--brand-colors-neutral-200: #f8f8fb;--brand-colors-neutral-100: #fafafa;--brand-colors-neutral-white: #ffffff;--brand-colors-blue-900: #043059;--brand-colors-blue-800: #082f75;--brand-colors-blue-700: #0c3b8d;--brand-colors-blue-600: #0645b1;--brand-colors-blue-500: #386ac1;--brand-colors-blue-400: #cddaef;--brand-colors-blue-300: #e6ecf7;--brand-colors-blue-200: #eef2f9;--brand-colors-blue-100: #f4f7fc;--brand-colors-gold-500: #877440;--brand-colors-gold-400: #e9e3d4;--brand-colors-gold-300: #f2efe8;--brand-colors-gold-200: #f9f6ed;--brand-colors-gold-100: #f9f7f4;--brand-colors-error-900: #920000;--brand-colors-error-500: #b60000;--brand-colors-success-900: #035c0f;--brand-colors-green: #ccffd4;--brand-colors-turquoise: #ccf7ff;--brand-colors-yellow: #f7ffcc;--brand-colors-peach: #ffd4cc;--brand-colors-violet: #f7ccff;--brand-colors-error-100: #fff2f2;--brand-colors-success-500: #05b01c;--brand-colors-success-100: #f0f8f1;--text-secondary: #535366;--icon-white: #ffffff;--background-beige-darker: #f2efe8;--icon-dark-grey: #535366;--type-font-family-sans-serif: DM Sans;--type-font-family-serif: Gupter;--type-font-family-mono: IBM Plex Mono;--type-weights-300: 300;--type-weights-400: 400;--type-weights-500: 500;--type-weights-700: 700;--type-sizes-12: 12px;--type-sizes-14: 14px;--type-sizes-16: 16px;--type-sizes-18: 18px;--type-sizes-20: 20px;--type-sizes-22: 22px;--type-sizes-24: 24px;--type-sizes-28: 28px;--type-sizes-30: 30px;--type-sizes-32: 32px;--type-sizes-40: 40px;--type-sizes-42: 42px;--type-sizes-48-2: 48px;--type-line-heights-16: 16px;--type-line-heights-20: 20px;--type-line-heights-23: 23px;--type-line-heights-24: 24px;--type-line-heights-25: 25px;--type-line-heights-26: 26px;--type-line-heights-29: 29px;--type-line-heights-30: 30px;--type-line-heights-32: 32px;--type-line-heights-34: 34px;--type-line-heights-35: 35px;--type-line-heights-36: 36px;--type-line-heights-38: 38px;--type-line-heights-40: 40px;--type-line-heights-46: 46px;--type-line-heights-48: 48px;--type-line-heights-52: 52px;--type-line-heights-58: 58px;--type-line-heights-68: 68px;--type-line-heights-74: 74px;--type-line-heights-82: 82px;--type-paragraph-spacings-0: 0px;--type-paragraph-spacings-4: 4px;--type-paragraph-spacings-8: 8px;--type-paragraph-spacings-16: 16px;--type-sans-serif-xl-font-weight: 400;--type-sans-serif-xl-size: 42px;--type-sans-serif-xl-line-height: 46px;--type-sans-serif-xl-paragraph-spacing: 16px;--type-sans-serif-lg-font-weight: 400;--type-sans-serif-lg-size: 32px;--type-sans-serif-lg-line-height: 38px;--type-sans-serif-lg-paragraph-spacing: 16px;--type-sans-serif-md-font-weight: 400;--type-sans-serif-md-line-height: 34px;--type-sans-serif-md-paragraph-spacing: 16px;--type-sans-serif-md-size: 28px;--type-sans-serif-xs-font-weight: 700;--type-sans-serif-xs-line-height: 25px;--type-sans-serif-xs-paragraph-spacing: 0px;--type-sans-serif-xs-size: 20px;--type-sans-serif-sm-font-weight: 400;--type-sans-serif-sm-line-height: 30px;--type-sans-serif-sm-paragraph-spacing: 16px;--type-sans-serif-sm-size: 24px;--type-body-xl-font-weight: 400;--type-body-xl-size: 24px;--type-body-xl-line-height: 36px;--type-body-xl-paragraph-spacing: 0px;--type-body-sm-font-weight: 400;--type-body-sm-size: 14px;--type-body-sm-line-height: 20px;--type-body-sm-paragraph-spacing: 8px;--type-body-xs-font-weight: 400;--type-body-xs-size: 12px;--type-body-xs-line-height: 16px;--type-body-xs-paragraph-spacing: 0px;--type-body-md-font-weight: 400;--type-body-md-size: 16px;--type-body-md-line-height: 20px;--type-body-md-paragraph-spacing: 4px;--type-body-lg-font-weight: 400;--type-body-lg-size: 20px;--type-body-lg-line-height: 26px;--type-body-lg-paragraph-spacing: 16px;--type-body-lg-medium-font-weight: 500;--type-body-lg-medium-size: 20px;--type-body-lg-medium-line-height: 32px;--type-body-lg-medium-paragraph-spacing: 16px;--type-body-md-medium-font-weight: 500;--type-body-md-medium-size: 16px;--type-body-md-medium-line-height: 20px;--type-body-md-medium-paragraph-spacing: 4px;--type-body-sm-bold-font-weight: 700;--type-body-sm-bold-size: 14px;--type-body-sm-bold-line-height: 20px;--type-body-sm-bold-paragraph-spacing: 8px;--type-body-sm-medium-font-weight: 500;--type-body-sm-medium-size: 14px;--type-body-sm-medium-line-height: 20px;--type-body-sm-medium-paragraph-spacing: 8px;--type-serif-md-font-weight: 400;--type-serif-md-size: 40px;--type-serif-md-paragraph-spacing: 0px;--type-serif-md-line-height: 48px;--type-serif-sm-font-weight: 400;--type-serif-sm-size: 28px;--type-serif-sm-paragraph-spacing: 0px;--type-serif-sm-line-height: 32px;--type-serif-lg-font-weight: 400;--type-serif-lg-size: 58px;--type-serif-lg-paragraph-spacing: 0px;--type-serif-lg-line-height: 68px;--type-serif-xs-font-weight: 400;--type-serif-xs-size: 18px;--type-serif-xs-line-height: 24px;--type-serif-xs-paragraph-spacing: 0px;--type-serif-xl-font-weight: 400;--type-serif-xl-size: 74px;--type-serif-xl-paragraph-spacing: 0px;--type-serif-xl-line-height: 82px;--type-mono-md-font-weight: 400;--type-mono-md-size: 22px;--type-mono-md-line-height: 24px;--type-mono-md-paragraph-spacing: 0px;--type-mono-lg-font-weight: 400;--type-mono-lg-size: 40px;--type-mono-lg-line-height: 40px;--type-mono-lg-paragraph-spacing: 0px;--type-mono-sm-font-weight: 400;--type-mono-sm-size: 14px;--type-mono-sm-line-height: 24px;--type-mono-sm-paragraph-spacing: 0px;--spacing-xs-4: 4px;--spacing-xs-8: 8px;--spacing-xs-16: 16px;--spacing-sm-24: 24px;--spacing-sm-32: 32px;--spacing-md-40: 40px;--spacing-md-48: 48px;--spacing-lg-64: 64px;--spacing-lg-80: 80px;--spacing-xlg-104: 104px;--spacing-xlg-152: 152px;--spacing-xs-12: 12px;--spacing-page-section: 152px;--spacing-card-list-spacing: 48px;--spacing-text-section-spacing: 80px;--spacing-md-xs-headings: 40px;--corner-radius-radius-lg: 16px;--corner-radius-radius-sm: 4px;--corner-radius-radius-md: 8px;--corner-radius-radius-round: 104px}}</style><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/single_work_page/loswp-fd2fcde21889491abfafcac2e33d795c8d15f5c18207be857e53e09b77f94215.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/body-170d1319f0e354621e81ca17054bb147da2856ec0702fe440a99af314a6338c5.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/button-8c9ae4b5c8a2531640c354d92a1f3579c8ff103277ef74913e34c8a76d4e6c00.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/heading-95367dc03b794f6737f30123738a886cf53b7a65cdef98a922a98591d60063e3.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/text_button-d1941ab08e91e29ee143084c4749da4aaffa350a2ac6eec2306b1d7a352d911a.css" /><link crossorigin="" href="https://fonts.gstatic.com/" rel="preconnect" /><link href="https://fonts.googleapis.com/css2?family=DM+Sans:ital,opsz,wght@0,9..40,100..1000;1,9..40,100..1000&amp;family=Gupter:wght@400;500;700&amp;family=IBM+Plex+Mono:wght@300;400&amp;family=Material+Symbols+Outlined:opsz,wght,FILL,GRAD@20,400,0,0&amp;display=swap" rel="stylesheet" /> </head> <body> <div id='react-modal'></div> <div class="js-upgrade-ie-banner" style="display: none; text-align: center; padding: 8px 0; background-color: #ebe480;"><p style="color: #000; font-size: 12px; margin: 0 0 4px;">Academia.edu no longer supports Internet Explorer.</p><p style="color: #000; font-size: 12px; margin: 0;">To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to&nbsp;<a href="https://www.academia.edu/upgrade-browser">upgrade your browser</a>.</p></div><script>// Show this banner for all versions of IE if (!!window.MSInputMethodContext || /(MSIE)/.test(navigator.userAgent)) { document.querySelector('.js-upgrade-ie-banner').style.display = 'block'; }</script> <div class="bootstrap login"><div class="modal fade login-modal" id="login-modal"><div class="login-modal-dialog modal-dialog"><div class="modal-content"><div class="modal-header"><button class="close close" data-dismiss="modal" type="button"><span aria-hidden="true">&times;</span><span class="sr-only">Close</span></button><h4 class="modal-title text-center"><strong>Log In</strong></h4></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><button class="btn btn-fb btn-lg btn-block btn-v-center-content" id="login-facebook-oauth-button"><svg style="float: left; width: 19px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="facebook-square" class="svg-inline--fa fa-facebook-square fa-w-14" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path fill="currentColor" d="M400 32H48A48 48 0 0 0 0 80v352a48 48 0 0 0 48 48h137.25V327.69h-63V256h63v-54.64c0-62.15 37-96.48 93.67-96.48 27.14 0 55.52 4.84 55.52 4.84v61h-31.27c-30.81 0-40.42 19.12-40.42 38.73V256h68.78l-11 71.69h-57.78V480H400a48 48 0 0 0 48-48V80a48 48 0 0 0-48-48z"></path></svg><small><strong>Log in</strong> with <strong>Facebook</strong></small></button><br /><button class="btn btn-google btn-lg btn-block btn-v-center-content" id="login-google-oauth-button"><svg style="float: left; width: 22px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="google-plus" class="svg-inline--fa fa-google-plus fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256,8C119.1,8,8,119.1,8,256S119.1,504,256,504,504,392.9,504,256,392.9,8,256,8ZM185.3,380a124,124,0,0,1,0-248c31.3,0,60.1,11,83,32.3l-33.6,32.6c-13.2-12.9-31.3-19.1-49.4-19.1-42.9,0-77.2,35.5-77.2,78.1S142.3,334,185.3,334c32.6,0,64.9-19.1,70.1-53.3H185.3V238.1H302.2a109.2,109.2,0,0,1,1.9,20.7c0,70.8-47.5,121.2-118.8,121.2ZM415.5,273.8v35.5H380V273.8H344.5V238.3H380V202.8h35.5v35.5h35.2v35.5Z"></path></svg><small><strong>Log in</strong> with <strong>Google</strong></small></button><br /><style type="text/css">.sign-in-with-apple-button { width: 100%; height: 52px; border-radius: 3px; border: 1px solid black; cursor: pointer; } .sign-in-with-apple-button > div { margin: 0 auto; / This centers the Apple-rendered button horizontally }</style><script src="https://appleid.cdn-apple.com/appleauth/static/jsapi/appleid/1/en_US/appleid.auth.js" type="text/javascript"></script><div class="sign-in-with-apple-button" data-border="false" data-color="white" id="appleid-signin"><span &nbsp;&nbsp;="Sign Up with Apple" class="u-fs11"></span></div><script>AppleID.auth.init({ clientId: 'edu.academia.applesignon', scope: 'name email', redirectURI: 'https://www.academia.edu/sessions', state: "f6bc7a7e1cc312c8d17e500f3c2ef238936e4206c225c7b1eb0016c84b8805b6", });</script><script>// Hacky way of checking if on fast loswp if (window.loswp == null) { (function() { const Google = window?.Aedu?.Auth?.OauthButton?.Login?.Google; const Facebook = window?.Aedu?.Auth?.OauthButton?.Login?.Facebook; if (Google) { new Google({ el: '#login-google-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } if (Facebook) { new Facebook({ el: '#login-facebook-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } })(); }</script></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><div class="hr-heading login-hr-heading"><span class="hr-heading-text">or</span></div></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><form class="js-login-form" action="https://www.academia.edu/sessions" accept-charset="UTF-8" method="post"><input type="hidden" name="authenticity_token" value="zm3SmKGnHiyyangziqu28DoDqUR1H3DBH6JGpozHSph4nEeobr-2Ofjh8VZChUkBTM4r98eH91zFpduxXAYeXw" autocomplete="off" /><div class="form-group"><label class="control-label" for="login-modal-email-input" style="font-size: 14px;">Email</label><input class="form-control" id="login-modal-email-input" name="login" type="email" /></div><div class="form-group"><label class="control-label" for="login-modal-password-input" style="font-size: 14px;">Password</label><input class="form-control" id="login-modal-password-input" name="password" type="password" /></div><input type="hidden" name="post_login_redirect_url" id="post_login_redirect_url" value="https://www.academia.edu/974166/Knowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics" autocomplete="off" /><div class="checkbox"><label><input type="checkbox" name="remember_me" id="remember_me" value="1" checked="checked" /><small style="font-size: 12px; margin-top: 2px; display: inline-block;">Remember me on this computer</small></label></div><br><input type="submit" name="commit" value="Log In" class="btn btn-primary btn-block btn-lg js-login-submit" data-disable-with="Log In" /></br></form><script>typeof window?.Aedu?.recaptchaManagedForm === 'function' && window.Aedu.recaptchaManagedForm( document.querySelector('.js-login-form'), document.querySelector('.js-login-submit') );</script><small style="font-size: 12px;"><br />or <a data-target="#login-modal-reset-password-container" data-toggle="collapse" href="javascript:void(0)">reset password</a></small><div class="collapse" id="login-modal-reset-password-container"><br /><div class="well margin-0x"><form class="js-password-reset-form" action="https://www.academia.edu/reset_password" accept-charset="UTF-8" method="post"><input type="hidden" name="authenticity_token" value="xJgcEd2bXjqVdKe6NKAovruJKLBT9Xcnbzcu46QTxgJyaYkhEoP2L9__Lt_8jtdPzUSqA-Ft8Lq1MLP0dNKSxQ" autocomplete="off" /><p>Enter the email address you signed up with and we&#39;ll email you a reset link.</p><div class="form-group"><input class="form-control" name="email" type="email" /></div><input class="btn btn-primary btn-block g-recaptcha js-password-reset-submit" data-sitekey="6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj" type="submit" value="Email me a link" /></form></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/collapse-45805421cf446ca5adf7aaa1935b08a3a8d1d9a6cc5d91a62a2a3a00b20b3e6a.js"], function() { // from javascript_helper.rb $("#login-modal-reset-password-container").on("shown.bs.collapse", function() { $(this).find("input[type=email]").focus(); }); }); </script> </div></div></div><div class="modal-footer"><div class="text-center"><small style="font-size: 12px;">Need an account?&nbsp;<a rel="nofollow" href="https://www.academia.edu/signup">Click here to sign up</a></small></div></div></div></div></div></div><script>// If we are on subdomain or non-bootstrapped page, redirect to login page instead of showing modal (function(){ if (typeof $ === 'undefined') return; var host = window.location.hostname; if ((host === $domain || host === "www."+$domain) && (typeof $().modal === 'function')) { $("#nav_log_in").click(function(e) { // Don't follow the link and open the modal e.preventDefault(); $("#login-modal").on('shown.bs.modal', function() { $(this).find("#login-modal-email-input").focus() }).modal('show'); }); } })()</script> <div id="fb-root"></div><script>window.fbAsyncInit = function() { FB.init({ appId: "2369844204", version: "v8.0", status: true, cookie: true, xfbml: true }); // Additional initialization code. if (window.InitFacebook) { // facebook.ts already loaded, set it up. window.InitFacebook(); } else { // Set a flag for facebook.ts to find when it loads. window.academiaAuthReadyFacebook = true; } };</script> <div id="google-root"></div><script>window.loadGoogle = function() { if (window.InitGoogle) { // google.ts already loaded, set it up. window.InitGoogle("331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"); } else { // Set a flag for google.ts to use when it loads. window.GoogleClientID = "331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"; } };</script> <div class="header--container" id="main-header-container"><div class="header--inner-container header--inner-container-ds2"><div class="header-ds2--left-wrapper"><div class="header-ds2--left-wrapper-inner"><a data-main-header-link-target="logo_home" href="https://www.academia.edu/"><img class="hide-on-desktop-redesign" style="height: 24px; width: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015-A.svg" width="24" height="24" /><img width="145.2" height="18" class="hide-on-mobile-redesign" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015.svg" /></a><div class="header--search-container header--search-container-ds2"><form class="js-SiteSearch-form select2-no-default-pills" action="https://www.academia.edu/search" accept-charset="UTF-8" method="get"><svg style="width: 14px; height: 14px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="search" class="header--search-icon svg-inline--fa fa-search fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M505 442.7L405.3 343c-4.5-4.5-10.6-7-17-7H372c27.6-35.3 44-79.7 44-128C416 93.1 322.9 0 208 0S0 93.1 0 208s93.1 208 208 208c48.3 0 92.7-16.4 128-44v16.3c0 6.4 2.5 12.5 7 17l99.7 99.7c9.4 9.4 24.6 9.4 33.9 0l28.3-28.3c9.4-9.4 9.4-24.6.1-34zM208 336c-70.7 0-128-57.2-128-128 0-70.7 57.2-128 128-128 70.7 0 128 57.2 128 128 0 70.7-57.2 128-128 128z"></path></svg><input class="header--search-input header--search-input-ds2 js-SiteSearch-form-input" data-main-header-click-target="search_input" name="q" placeholder="Search" type="text" /></form></div></div></div><nav class="header--nav-buttons header--nav-buttons-ds2 js-main-nav"><button class="ds2-5-button ds2-5-button--secondary js-header-login-url header-button-ds2 header-login-ds2 hide-on-mobile-redesign react-login-modal-opener" data-signup-modal="{&quot;location&quot;:&quot;login-button--header&quot;}" rel="nofollow">Log In</button><button class="ds2-5-button ds2-5-button--secondary header-button-ds2 hide-on-mobile-redesign react-login-modal-opener" data-signup-modal="{&quot;location&quot;:&quot;signup-button--header&quot;}" rel="nofollow">Sign Up</button><button class="header--hamburger-button header--hamburger-button-ds2 hide-on-desktop-redesign js-header-hamburger-button"><div class="icon-bar"></div><div class="icon-bar" style="margin-top: 4px;"></div><div class="icon-bar" style="margin-top: 4px;"></div></button></nav></div><ul class="header--dropdown-container js-header-dropdown"><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/login" rel="nofollow">Log In</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/signup" rel="nofollow">Sign Up</a></li><li class="header--dropdown-row js-header-dropdown-expand-button"><button class="header--dropdown-button">more<svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="caret-down" class="header--dropdown-button-icon svg-inline--fa fa-caret-down fa-w-10" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path fill="currentColor" d="M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z"></path></svg></button></li><li><ul class="header--expanded-dropdown-container"><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/about">About</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/press">Press</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/documents">Papers</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/terms">Terms</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/privacy">Privacy</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/copyright">Copyright</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://www.academia.edu/hiring"><svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="header--dropdown-row-icon svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg>We&#39;re Hiring!</a></li><li class="header--dropdown-row"><a class="header--dropdown-link" href="https://support.academia.edu/hc/en-us"><svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="header--dropdown-row-icon svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg>Help Center</a></li><li class="header--dropdown-row js-header-dropdown-collapse-button"><button class="header--dropdown-button">less<svg aria-hidden="true" focusable="false" data-prefix="fas" data-icon="caret-up" class="header--dropdown-button-icon svg-inline--fa fa-caret-up fa-w-10" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path fill="currentColor" d="M288.662 352H31.338c-17.818 0-26.741-21.543-14.142-34.142l128.662-128.662c7.81-7.81 20.474-7.81 28.284 0l128.662 128.662c12.6 12.599 3.676 34.142-14.142 34.142z"></path></svg></button></li></ul></li></ul></div> <script src="//a.academia-assets.com/assets/webpack_bundles/fast_loswp-bundle-a382613945ae46ec77bb6b8a480081f38f18faa087486ce66e9aac9d3723f9c0.js" defer="defer"></script><script>window.loswp = {}; window.loswp.author = 808988; window.loswp.bulkDownloadFilterCounts = {}; window.loswp.hasDownloadableAttachment = true; window.loswp.hasViewableAttachments = true; // TODO: just use routes for this window.loswp.loginUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F974166%2FKnowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics%3Fauto%3Ddownload"; window.loswp.translateUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F974166%2FKnowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics%3Fshow_translation%3Dtrue"; window.loswp.previewableAttachments = [{"id":5958495,"identifier":"Attachment_5958495","shouldShowBulkDownload":false}]; window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":974166,"created_at":"2011-10-03T05:10:51.570-07:00","from_world_paper_id":18050738,"updated_at":"2025-01-12T01:57:30.957-08:00","_data":{"ai_abstract":"This paper explores knowledge abstraction in reinforcement learning (RL) and its application to robotics, addressing challenges related to the expansive state space in real-world environments. It presents new methods to develop high-level abstractions automatically, thereby reducing state dimensions and improving learning processes in RL. Key methodologies include enhancing existing algorithms and proposing novel approaches to incorporate knowledge abstraction effectively, ultimately aiming to optimize the training of agents in robotic tasks.","publication_name":"cs.qub.ac.uk"},"document_type":"paper","pre_hit_view_count_baseline":0,"quality":"high","language":"en","title":"Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [808988]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;swp-splash-paper-cover&quot;,&quot;attachmentId&quot;:5958495,&quot;attachmentType&quot;:&quot;pdf&quot;}"><img alt="First page of “Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/5958495/mini_magick20190427-11529-7meli0.png?1556371460" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Knowledge Abstraction in Reinforcement Learning and Its Application on Robotics</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="808988" href="https://columbia.academia.edu/ZhihuiLuo"><img alt="Profile image of Zhi-hui Luo" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Zhi-hui Luo</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">cs.qub.ac.uk</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">12 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 974166; const worksViewsPath = "/v0/works/views?subdomain_param=api&amp;work_ids%5B%5D=974166"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--detail ds2-5-body-md">AI-generated Abstract</p><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">This paper explores knowledge abstraction in reinforcement learning (RL) and its application to robotics, addressing challenges related to the expansive state space in real-world environments. It presents new methods to develop high-level abstractions automatically, thereby reducing state dimensions and improving learning processes in RL. Key methodologies include enhancing existing algorithms and proposing novel approaches to incorporate knowledge abstraction effectively, ultimately aiming to optimize the training of agents in robotic tasks.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;continue-reading-button--work-card&quot;,&quot;attachmentId&quot;:5958495,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:&quot;https://www.academia.edu/974166/Knowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics&quot;}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;download-pdf-button--work-card&quot;,&quot;attachmentId&quot;:5958495,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:&quot;https://www.academia.edu/974166/Knowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics&quot;}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas" data-impression-entity-id="974166" data-impression-entity-type="2" data-impression-source="signup-banner"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;signup-banner&quot;}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. If the signup banner trigger (a 242px-high* invisible div underneath the 'See Full PDF' / 'Download PDF' buttons) // is already fully scrolled above the viewport, show the banner by default // 2. If the signup banner trigger is fully visible, show the banner // 3. If the signup banner trigger has even a few pixels scrolled below the viewport, hide the banner // // * 242px is the empirically determined height of the signup banner. It's better to be a bit taller than // necessary than too short, so it's fine that the mobile (small breakpoint) banner is shorter. // First check session storage for the signup banner's visibility state const signupBannerHidden = sessionStorage.getItem('ds-signup-banner-hidden'); if (signupBannerHidden === 'true') { return; } const signupBanner = document.querySelector('.ds-signup-banner'); const signupBannerTrigger = document.querySelector('.ds-signup-banner-trigger'); if (!signupBannerTrigger) { window.Sentry.captureMessage("Signup banner trigger not found"); return; } let footerShown = false; window.addEventListener('load', () => { const rect = signupBannerTrigger.getBoundingClientRect(); // If page loaded up already scrolled below the trigger (via scroll restoration), show the banner by default if (rect.bottom < 0) { footerShown = true; signupBanner.classList.add('ds-signup-banner-visible'); } }); // Wait for trigger to fully enter viewport before showing banner (ensures PDF CTAs are never covered by banner) const observer = new IntersectionObserver((entries) => { entries.forEach(entry => { if (entry.isIntersecting && !footerShown) { footerShown = true; signupBanner.classList.add('ds-signup-banner-visible'); } else if (!entry.isIntersecting && footerShown) { if (signupBannerTrigger.getBoundingClientRect().bottom > 0) { footerShown = false; signupBanner.classList.remove('ds-signup-banner-visible'); } } }); }); observer.observe(signupBannerTrigger); // Set up signup banner close button event handler: const signupBannerCloseButton = document.querySelector('#ds-signup-banner-close-button'); signupBannerCloseButton.addEventListener('click', () => { signupBanner.classList.remove('ds-signup-banner-visible'); observer.unobserve(signupBannerTrigger); // Store the signup banner's visibility state in session storage sessionStorage.setItem('ds-signup-banner-hidden', 'true'); }); })();</script></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="5958495" data-landing_url="https://www.academia.edu/974166/Knowledge_Abstraction_in_Reinforcement_Learning_and_Its_Application_on_Robotics" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="116034535" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/116034535/Reinforcement_Learning_with_Knowledge_Representation_and_Reasoning_A_Brief_Survey">Reinforcement Learning with Knowledge Representation and Reasoning: A Brief Survey</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="19778881" href="https://independent.academia.edu/HankzHankuiZhuo">Hankz Hankui Zhuo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2023</p><p class="ds-related-work--abstract ds2-5-body-sm">Reinforcement Learning (RL) has achieved tremendous development in recent years, but still faces significant obstacles in addressing complex reallife problems due to the issues of poor system generalization, low sample efficiency as well as safety and interpretability concerns. The core reason underlying such dilemmas can be attributed to the fact that most of the work has focused on the computational aspect of value functions or policies using a representational model to describe atomic components of rewards, states and actions etc, thus neglecting the rich high-level declarative domain knowledge of facts, relations and rules that can be either provided a priori or acquired through reasoning over time. Recently, there has been a rapidly growing interest in the use of Knowledge Representation and Reasoning (KRR) methods, usually using logical languages, to enable more abstract representation and efficient learning in RL. In this survey, we provide a preliminary overview on these endeavors that leverage the strengths of KRR to help solving various problems in RL, and discuss the challenging open problems and possible directions for future work in this area.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Reinforcement Learning with Knowledge Representation and Reasoning: A Brief Survey&quot;,&quot;attachmentId&quot;:112276912,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/116034535/Reinforcement_Learning_with_Knowledge_Representation_and_Reasoning_A_Brief_Survey&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/116034535/Reinforcement_Learning_with_Knowledge_Representation_and_Reasoning_A_Brief_Survey"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="75003419" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/75003419/Using_background_knowledge_to_speed_reinforcement_learning_in_physical_agents">Using background knowledge to speed reinforcement learning in physical agents</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="41768183" href="https://independent.academia.edu/DanielShapiro4">Daniel Shapiro</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the fifth international conference on Autonomous agents - AGENTS &#39;01, 2001</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper describes Icarus, an agent architecture that embeds a hierarchical reinforcement learning algorithm within a language for specifying agent behavior. An Icarus program expresses an approximately correct theory about how to behave with options at varying levels of detail, while the Icarus agent determines the best options by learning from experience. We describe Icarus and its learning algorithm, then report on two experiments in a vehicle control domain. The first examines the benefit of new distinctions about state, whereas the second explores the impact of added plan structure. We show that background knowledge increases learning rate and asymptotic performance, and decreases plan size by three orders of magnitude, relative to the typical formulation of the learning problem in our test domain.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Using background knowledge to speed reinforcement learning in physical agents&quot;,&quot;attachmentId&quot;:82948929,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/75003419/Using_background_knowledge_to_speed_reinforcement_learning_in_physical_agents&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/75003419/Using_background_knowledge_to_speed_reinforcement_learning_in_physical_agents"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="50599664" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/50599664/Scaling_up_reinforcement_learning_with_a_relational_representation">Scaling up reinforcement learning with a relational representation</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="15097714" href="https://independent.academia.edu/EduardoMorales7">Eduardo Morales</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2003</p><p class="ds-related-work--abstract ds2-5-body-sm">Reinforcement learning has been repeatedly suggested as good candidate for learning in robotics. However, the large search spaces normally occurring robotics and expensive training experiences required by reinforcement learning algorithms has hampered its applicability. This paper introduces a new approach for reinforcement learning based on a relational representation which: (i) can be applied over large search spaces, (ii) can incorporate domain knowledge, and (iii) can use previously learned policies on different, although similar, problems. In the proposed framework states are represented as sets of first order relations, actions in terms of those relations, and policies are learned over such generalized representation. It is shown how this representation can capture large search spaces with a relatively small set of actions and states, and that policies learned over this generalized representation can be directly apply to other problems which can be characterized by the same set of relations.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Scaling up reinforcement learning with a relational representation&quot;,&quot;attachmentId&quot;:68520915,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/50599664/Scaling_up_reinforcement_learning_with_a_relational_representation&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/50599664/Scaling_up_reinforcement_learning_with_a_relational_representation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="974170" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/974170/Hierarchical_Abstraction_in_Reinforcement_Learning_Based_on_Feature_Discovery">Hierarchical Abstraction in Reinforcement Learning Based on Feature Discovery</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="808988" href="https://columbia.academia.edu/ZhihuiLuo">Zhi-hui Luo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Hierarchical Abstraction in Reinforcement Learning Based on Feature Discovery&quot;,&quot;attachmentId&quot;:5958494,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/974170/Hierarchical_Abstraction_in_Reinforcement_Learning_Based_on_Feature_Discovery&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/974170/Hierarchical_Abstraction_in_Reinforcement_Learning_Based_on_Feature_Discovery"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="21440038" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/21440038/Incorporating_prior_knowledge_and_previously_learned_information_into_reinforcement_learning_agents">Incorporating prior knowledge and previously learned information into reinforcement learning agents</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="42517459" href="https://independent.academia.edu/PKhosla">Pradeep Khosla</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2000</p><p class="ds-related-work--abstract ds2-5-body-sm">Reinforcement learning has received much attention in the past decade. The primary thrust of this research has focused on tabula rasa learning methods. That is, the learning agent is initially unaware of its environment and must learn or re-learn everything. We feel that this is neither realistic nor effective. While the agent may start out with little or no knowledge of its environment, it must be able to incorporate new information into the learning of subsequent tasks otherwise the learning effort is largely wasted. To address the shortcomings of tabula rasa learning, we present a general and intuitive approach for incorporating previously learned information and prior knowledge into the reinforcement learning process. We demonstrate the potential of this method on learning problems in the mobilerobot and grid-world domains, where results indicate that learning time can be decreased. We also demonstrate that multiple knowledge sources can be incorporated into the learning process.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Incorporating prior knowledge and previously learned information into reinforcement learning agents&quot;,&quot;attachmentId&quot;:41876167,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/21440038/Incorporating_prior_knowledge_and_previously_learned_information_into_reinforcement_learning_agents&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/21440038/Incorporating_prior_knowledge_and_previously_learned_information_into_reinforcement_learning_agents"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="18975522" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/18975522/Structural_knowledge_transfer_by_spatial_abstraction_for_reinforcement_learning_agents">Structural knowledge transfer by spatial abstraction for reinforcement learning agents</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="39120946" href="https://independent.academia.edu/DiedrichWolter">Diedrich Wolter</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Adaptive Behavior, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">In this article we investigate the role of abstraction principles for knowledge transfer in agent control learning tasks. We analyze abstraction from a formal point of view and characterize three distinct facets: aspectualization, coarsening, and conceptual classification. The taxonomy we develop allows us to interrelate existing approaches to abstraction, leading to a code of practice for designing knowledge representations that support knowledge transfer. We detail how aspectualization can be utilized to achieve knowledge transfer in reinforcement learning. We propose the use of so-called structure space aspectualizable knowledge representations that explicate structural properties of the state space and present a posteriori structure space aspectualization (APSST) as a method to extract generally sensible behavior from a learned policy. This new policy can be used for knowledge transfer to support learning new tasks in different environments. Finally, we present a case study that demonstrates transfer of generally sensible navigation skills from simple simulation to a real-world robotic platform.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Structural knowledge transfer by spatial abstraction for reinforcement learning agents&quot;,&quot;attachmentId&quot;:40361544,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/18975522/Structural_knowledge_transfer_by_spatial_abstraction_for_reinforcement_learning_agents&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/18975522/Structural_knowledge_transfer_by_spatial_abstraction_for_reinforcement_learning_agents"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="974168" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/974168/Temporal_Abstraction_in_Reinforcement_Learning_Based_on_Environmental_Feature">Temporal Abstraction in Reinforcement Learning Based on Environmental Feature</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="808988" href="https://columbia.academia.edu/ZhihuiLuo">Zhi-hui Luo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2008</p><p class="ds-related-work--abstract ds2-5-body-sm">Reinforcement learning offers a fundamental framework for intelligent agents to improve their behavior through interacting with the environment. In many problem domains related to sequential decision making, reinforcement learning has shown higher standard of performance than other learning methods. However, as the complexity of problems grow, the traditional reinforcement learning approach becomes increasing inefficient. It struggles when faced with the &quot;explosion&quot; of the state space. The success of applying reinforcement learning to complex problems depends heavily on good abstraction methods in order to reduce the state dimensions. This thesis concentrates on developing methods to address this open IV I enjoy and value the friendships and associations established, past and present, in Queen&#39;s University Belfast: This thesis is dedicated to my caring and supporting family. Deep thanks to my dearest sister and also my best friend, Weiwei Liu, who took care of my daily life and setup an excellent example of dedication for academic research. Special thanks to my aunty, Qiaohua Luo, who shares enthusiastically mentorship, spiritual encouraging and supports financially for my life. My dear parents have been a source of love, care and support. It wouldn&#39;t be possible for all this without them. Finally, I would also like to express my gratitude to my grandpas and grandmas, for their love, care and guidance.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Temporal Abstraction in Reinforcement Learning Based on Environmental Feature&quot;,&quot;attachmentId&quot;:5958496,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/974168/Temporal_Abstraction_in_Reinforcement_Learning_Based_on_Environmental_Feature&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/974168/Temporal_Abstraction_in_Reinforcement_Learning_Based_on_Environmental_Feature"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="6554273" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/6554273/Between_MDPs_and_Semi_MDPs_A_Framework_for_Temporal_Abstraction_in_Reinforcement_Learning">Between MDPs and Semi-MDPs: A Framework for Temporal Abstraction in Reinforcement Learning</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="10517822" href="https://mduroktak.academia.edu/SatinderSingh">Satinder Singh</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Artificial Intelligence, 1999</p><p class="ds-related-work--abstract ds2-5-body-sm">Learning, planning, and representing knowledge at multiple levels of temporal abstraction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforcement learning and Markov decision processes (MDPs). We extend the usual notion of action in this framework to include options-closed-loop policies for taking action over a period of time. Examples of options include picking up an object, going to lunch, and traveling to a distant city, as well as primitive actions such as muscle twitches and joint torques. Overall, we show that options enable temporally abstract knowledge and action to be included in the reinforcement learning framework in a natural and general way. In particular, we show that options may be used interchangeably with primitive actions in planning methods such as dynamic programming and in learning methods such as Q-learning. Formally, a set of options defined over an MDP constitutes a semi-Markov decision process (SMDP), and the theory of SMDPs provides the foundation for the theory of options. However, the most interesting issues concern the interplay between the underlying MDP and the SMDP and are thus beyond SMDP theory. We present results for three such cases: (1) we show that the results of planning with options can be used during execution to interrupt options and thereby perform even better than planned, (2) we introduce new intra-option methods that are able to learn about an option from fragments of its execution, and (3) we propose a notion of subgoal that can be used to improve the options themselves. All of these results have precursors in the existing literature; the contribution of this paper is to establish them in a simpler and more general setting with fewer changes to the existing reinforcement learning framework. In particular, we show that these results can be obtained without committing to (or ruling out) any particular approach to state abstraction, hierarchy, function approximation, or the macroutility problem. : S 0 0 0 4 -3 7 0 2 ( 9 9 ) 0 0 0 5 2 -1 182 R.S. Sutton et al. / Artificial Intelligence 112 (1999)</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Between MDPs and Semi-MDPs: A Framework for Temporal Abstraction in Reinforcement Learning&quot;,&quot;attachmentId&quot;:48811297,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/6554273/Between_MDPs_and_Semi_MDPs_A_Framework_for_Temporal_Abstraction_in_Reinforcement_Learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/6554273/Between_MDPs_and_Semi_MDPs_A_Framework_for_Temporal_Abstraction_in_Reinforcement_Learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="53493936" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/53493936/Accelerating_reinforcement_learning_by_reusing_abstract_policies">Accelerating reinforcement learning by reusing abstract policies</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="121862354" href="https://independent.academia.edu/YannickBergamo">Yannick Bergamo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2011</p><p class="ds-related-work--abstract ds2-5-body-sm">Reinforcement learning (RL) provides a general approach for developing intelligent agents that are able to optimize their behaviors in stochastic environments. Unfortunately, most work in RL is based on propositional representations, making it difficult to apply it to more complex real-world tasks in which states and actions are more naturally represented in relational form. Moreover, most work in RL does not take into account existing solutions to similar problems when learning a policy to solve a new problem, and consequently solves the new problem from scratch, what can be very time consuming. In this article we explore the powerful possibilities of using relational descriptions so that we can learn abstract policies, and in reusing these policies to improve initial performance of an RL learner in a similar new problem. Experiments carried out attest the effectiveness of our proposal.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Accelerating reinforcement learning by reusing abstract policies&quot;,&quot;attachmentId&quot;:70312004,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/53493936/Accelerating_reinforcement_learning_by_reusing_abstract_policies&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/53493936/Accelerating_reinforcement_learning_by_reusing_abstract_policies"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="15153013" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/15153013/Reduction_of_Learning_Time_for_Robots_Using_Automatic_State_Abstraction">Reduction of Learning Time for Robots Using Automatic State Abstraction</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="34192914" href="https://ethz.academia.edu/RSiegwart">Roland Siegwart</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Springer Tracts in Advanced Robotics, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">The required learning time and curse of dimensionality restrict the applicability of Reinforcement Learning(RL) on real robots. Difficulty in inclusion of initial knowledge and understanding the learned rules must be added to the mentioned problems. In this paper we address automatic state abstraction and creation of hierarchies in RL agent&#39;s mind, as two major approaches for reducing the number of learning trials, simplifying inclusion of prior knowledge, and making the learned rules more abstract and understandable. We formalize automatic state abstraction and hierarchy creation as an optimization problem and derive a new algorithm that adapts decision tree learning techniques to state abstraction. The proof of performance is supported by strong evidences from simulation results in nondeterministic environments. Simulation results show encouraging enhancements in the required number of learning trials, agent&#39;s performance, size of the learned trees, and computation time of the algorithm.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Reduction of Learning Time for Robots Using Automatic State Abstraction&quot;,&quot;attachmentId&quot;:43526772,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/15153013/Reduction_of_Learning_Time_for_Robots_Using_Automatic_State_Abstraction&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/15153013/Reduction_of_Learning_Time_for_Robots_Using_Automatic_State_Abstraction"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;continue-reading-button--sticky-ctas&quot;,&quot;attachmentId&quot;:5958495,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;download-pdf-button--sticky-ctas&quot;,&quot;attachmentId&quot;:5958495,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_5958495" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="12892636" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/12892636/Algorithms_and_Representations_for_Reinforcement_Learning">Algorithms and Representations for Reinforcement Learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32039364" href="https://nust.academia.edu/jamesslate">james slate</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Algorithms and Representations for Reinforcement Learning&quot;,&quot;attachmentId&quot;:37869041,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/12892636/Algorithms_and_Representations_for_Reinforcement_Learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/12892636/Algorithms_and_Representations_for_Reinforcement_Learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="1" data-entity-id="118454982" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/118454982/Learning_to_Predict_Consequences_as_a_Method_of_Knowledge_Transfer_in_Reinforcement_Learning">Learning to Predict Consequences as a Method of Knowledge Transfer in Reinforcement Learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="303040044" href="https://independent.academia.edu/EricChalmers1">Eric Chalmers</a></div><p class="ds-related-work--metadata ds2-5-body-xs">IEEE transactions on neural networks and learning systems, 2017</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Learning to Predict Consequences as a Method of Knowledge Transfer in Reinforcement Learning&quot;,&quot;attachmentId&quot;:114077575,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/118454982/Learning_to_Predict_Consequences_as_a_Method_of_Knowledge_Transfer_in_Reinforcement_Learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/118454982/Learning_to_Predict_Consequences_as_a_Method_of_Knowledge_Transfer_in_Reinforcement_Learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="2" data-entity-id="120302922" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/120302922/Relational_Concepts_in_Deep_Reinforcement_Learning_Emergence_and_Representation">Relational Concepts in Deep Reinforcement Learning: Emergence and Representation</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="41961965" href="https://independent.academia.edu/HorstmichaelGross">Horst-michael Gross</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2020</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Relational Concepts in Deep Reinforcement Learning: Emergence and Representation&quot;,&quot;attachmentId&quot;:115497717,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/120302922/Relational_Concepts_in_Deep_Reinforcement_Learning_Emergence_and_Representation&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/120302922/Relational_Concepts_in_Deep_Reinforcement_Learning_Emergence_and_Representation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="3" data-entity-id="120816182" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/120816182/Learning_to_Act_with_RVRL_Agents">Learning to Act with RVRL Agents</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="119202" href="https://royalholloway.academia.edu/kostas">Kostas Stathis</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2007</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Learning to Act with RVRL Agents&quot;,&quot;attachmentId&quot;:115847240,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/120816182/Learning_to_Act_with_RVRL_Agents&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/120816182/Learning_to_Act_with_RVRL_Agents"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="4" data-entity-id="32208886" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/32208886/Speeding_up_reinforcement_learning_through_abstraction_and_transfer_learning">Speeding-up reinforcement learning through abstraction and transfer learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="62405068" href="https://independent.academia.edu/AnnaCosta23">Anna Costa</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the 2013 International Conference on Autonomous Agents and Multi Agent Systems, 2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Speeding-up reinforcement learning through abstraction and transfer learning&quot;,&quot;attachmentId&quot;:52438086,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/32208886/Speeding_up_reinforcement_learning_through_abstraction_and_transfer_learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/32208886/Speeding_up_reinforcement_learning_through_abstraction_and_transfer_learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="5" data-entity-id="24456560" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/24456560/Hierarchical_Reinforcement_Learning_Learning_sub_goals_and_state_abstraction">Hierarchical Reinforcement Learning: Learning sub-goals and state-abstraction</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="11704225" href="https://iscte-iul.academia.edu/LNunes">Luís Nunes</a><span>, </span><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="47141903" href="https://iscte-iul.academia.edu/DavidJardim">David Jardim</a></div><p class="ds-related-work--metadata ds2-5-body-xs">6Th Iberian Conference on Information Systems and Technologies, 2011</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Hierarchical Reinforcement Learning: Learning sub-goals and state-abstraction&quot;,&quot;attachmentId&quot;:44788445,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/24456560/Hierarchical_Reinforcement_Learning_Learning_sub_goals_and_state_abstraction&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/24456560/Hierarchical_Reinforcement_Learning_Learning_sub_goals_and_state_abstraction"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="6" data-entity-id="253474" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/253474/RL_TOPs_An_Architecture_for_Modularity_and_Re_Use_In_Reinforcement_Learning">RL-TOPs: An Architecture for Modularity and Re-Use In Reinforcement Learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="163560" href="https://unsw.academia.edu/MalcolmRyan">Malcolm Ryan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proc. 15th International Conf. on Machine Learning, 1998</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;RL-TOPs: An Architecture for Modularity and Re-Use In Reinforcement Learning&quot;,&quot;attachmentId&quot;:3482413,&quot;attachmentType&quot;:&quot;eps&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/253474/RL_TOPs_An_Architecture_for_Modularity_and_Re_Use_In_Reinforcement_Learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/253474/RL_TOPs_An_Architecture_for_Modularity_and_Re_Use_In_Reinforcement_Learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="7" data-entity-id="253475" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/253475/Hierarchical_Reinforcement_Learning_a_Hybrid_Approach">Hierarchical Reinforcement Learning: a Hybrid Approach</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="163560" href="https://unsw.academia.edu/MalcolmRyan">Malcolm Ryan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2002</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Hierarchical Reinforcement Learning: a Hybrid Approach&quot;,&quot;attachmentId&quot;:3238290,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/253475/Hierarchical_Reinforcement_Learning_a_Hybrid_Approach&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/253475/Hierarchical_Reinforcement_Learning_a_Hybrid_Approach"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="67308762" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/67308762/Building_Relational_World_Models_for_Reinforcement_Learning">Building Relational World Models for Reinforcement Learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="155758897" href="https://independent.academia.edu/RMaclin">Richard Maclin</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Building Relational World Models for Reinforcement Learning&quot;,&quot;attachmentId&quot;:78173735,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/67308762/Building_Relational_World_Models_for_Reinforcement_Learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/67308762/Building_Relational_World_Models_for_Reinforcement_Learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="9" data-entity-id="15223246" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/15223246/A_hybrid_architecture_for_situated_learning_of_reactive_sequential_decision_making">A hybrid architecture for situated learning of reactive sequential decision making</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="34285799" href="https://independent.academia.edu/EdwardMerrill">Edward Merrill</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Applied Intelligence, 1999</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;A hybrid architecture for situated learning of reactive sequential decision making&quot;,&quot;attachmentId&quot;:43419249,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/15223246/A_hybrid_architecture_for_situated_learning_of_reactive_sequential_decision_making&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/15223246/A_hybrid_architecture_for_situated_learning_of_reactive_sequential_decision_making"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="10" data-entity-id="70133601" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/70133601/Option_Encoder_A_Framework_for_Discovering_a_Policy_Basis_in_Reinforcement_Learning">Option Encoder: A Framework for Discovering a Policy Basis in Reinforcement Learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="35235876" href="https://msec.academia.edu/arjunmanoharan">arjun manoharan</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2020</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Option Encoder: A Framework for Discovering a Policy Basis in Reinforcement Learning&quot;,&quot;attachmentId&quot;:79992734,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/70133601/Option_Encoder_A_Framework_for_Discovering_a_Policy_Basis_in_Reinforcement_Learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/70133601/Option_Encoder_A_Framework_for_Discovering_a_Policy_Basis_in_Reinforcement_Learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="11" data-entity-id="21440274" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/21440274/Incorporating_Prior_Knowledge_and_Previously_Learned_Information_into_Reinforcement_Learning">Incorporating Prior Knowledge and Previously Learned Information into Reinforcement Learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="42517459" href="https://independent.academia.edu/PKhosla">Pradeep Khosla</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2001</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Incorporating Prior Knowledge and Previously Learned Information into Reinforcement Learning&quot;,&quot;attachmentId&quot;:41876301,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/21440274/Incorporating_Prior_Knowledge_and_Previously_Learned_Information_into_Reinforcement_Learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/21440274/Incorporating_Prior_Knowledge_and_Previously_Learned_Information_into_Reinforcement_Learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="12" data-entity-id="124863007" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/124863007/Accelerating_Reinforcement_Learning_through_the_Discovery_of_Useful_Subgoals">Accelerating Reinforcement Learning through the Discovery of Useful Subgoals</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="67809175" href="https://independent.academia.edu/AndrewBarto">Andrew Barto</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2001</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Accelerating Reinforcement Learning through the Discovery of Useful Subgoals&quot;,&quot;attachmentId&quot;:119010147,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/124863007/Accelerating_Reinforcement_Learning_through_the_Discovery_of_Useful_Subgoals&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/124863007/Accelerating_Reinforcement_Learning_through_the_Discovery_of_Useful_Subgoals"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="13" data-entity-id="160776" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/160776/Programmable_Reinforcement_Learning_Agents">Programmable Reinforcement Learning Agents</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="13583" href="https://berkeley.academia.edu/StuartJRussell">Stuart J. Russell</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Programmable Reinforcement Learning Agents&quot;,&quot;attachmentId&quot;:71758,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/160776/Programmable_Reinforcement_Learning_Agents&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/160776/Programmable_Reinforcement_Learning_Agents"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="14" data-entity-id="102698888" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/102698888/Policyblocks_An_algorithm_for_creating_useful_macro_actions_in_reinforcement_learning">Policyblocks: An algorithm for creating useful macro-actions in reinforcement learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="67809175" href="https://independent.academia.edu/AndrewBarto">Andrew Barto</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2002</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Policyblocks: An algorithm for creating useful macro-actions in reinforcement learning&quot;,&quot;attachmentId&quot;:102899823,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/102698888/Policyblocks_An_algorithm_for_creating_useful_macro_actions_in_reinforcement_learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/102698888/Policyblocks_An_algorithm_for_creating_useful_macro_actions_in_reinforcement_learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="15" data-entity-id="5116380" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/5116380/Bridging_the_Gap_between_Reinforcement_Learning_and_Knowledge_Representation_A_Logical_Off_and_On_Policy_Framework">Bridging the Gap between Reinforcement Learning and Knowledge Representation: A Logical Off and On-Policy Framework</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="6875940" href="https://independent.academia.edu/emadsaad">emad saad</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Computing Research Repository, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Bridging the Gap between Reinforcement Learning and Knowledge Representation: A Logical Off and On-Policy Framework&quot;,&quot;attachmentId&quot;:49443010,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/5116380/Bridging_the_Gap_between_Reinforcement_Learning_and_Knowledge_Representation_A_Logical_Off_and_On_Policy_Framework&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/5116380/Bridging_the_Gap_between_Reinforcement_Learning_and_Knowledge_Representation_A_Logical_Off_and_On_Policy_Framework"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="16" data-entity-id="160766" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/160766/State_Abstraction_for_Programmable_Reinforcement_Learning_Agents">State Abstraction for Programmable Reinforcement Learning Agents</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="13583" href="https://berkeley.academia.edu/StuartJRussell">Stuart J. Russell</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;State Abstraction\nfor Programmable Reinforcement Learning Agents&quot;,&quot;attachmentId&quot;:71674,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/160766/State_Abstraction_for_Programmable_Reinforcement_Learning_Agents&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/160766/State_Abstraction_for_Programmable_Reinforcement_Learning_Agents"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="17" data-entity-id="2770592" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/2770592/A_Framework_for_Learning_and_Control_in_Intelligent">A Framework for Learning and Control in Intelligent</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="10006" href="https://umass.academia.edu/RodericAGrupen">Roderic A. Grupen</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;A Framework for Learning and Control in Intelligent&quot;,&quot;attachmentId&quot;:30748111,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/2770592/A_Framework_for_Learning_and_Control_in_Intelligent&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/2770592/A_Framework_for_Learning_and_Control_in_Intelligent"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="18" data-entity-id="96493310" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/96493310/An_Architecture_for_Behavior_Based_Reinforcement_Learning">An Architecture for Behavior-Based Reinforcement Learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="27840883" href="https://edinburgh.academia.edu/GillianHayes">Gillian Hayes</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Adaptive Behavior, 2005</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;An Architecture for Behavior-Based Reinforcement Learning&quot;,&quot;attachmentId&quot;:98377104,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/96493310/An_Architecture_for_Behavior_Based_Reinforcement_Learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/96493310/An_Architecture_for_Behavior_Based_Reinforcement_Learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="19" data-entity-id="630059" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/630059/Module_based_reinforcement_learning_Experiments_with_a_real_robot">Module-based reinforcement learning: Experiments with a real robot</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="462434" href="https://ualberta.academia.edu/CsabaSzepesvari">Csaba Szepesvari</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Machine Learning, 1998</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Module-based reinforcement learning: Experiments with a real robot&quot;,&quot;attachmentId&quot;:3406050,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/630059/Module_based_reinforcement_learning_Experiments_with_a_real_robot&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/630059/Module_based_reinforcement_learning_Experiments_with_a_real_robot"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="20" data-entity-id="4744200" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/4744200/Autonomous_learning_of_high_level_states_and_actions_in_continuous_environments">Autonomous learning of high-level states and actions in continuous environments. </a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="54159" href="https://umich.academia.edu/BenjaminKuipers">Benjamin Kuipers</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Jonathan Mugan and Benjamin Kuipers. 2012. Autonomous learning of high-level states and actions in continuous environments. IEEE Transactions on Autonomous Mental Development 4(1): 70-86, 2012., 2012</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;Autonomous learning of high-level states and actions in continuous environments. &quot;,&quot;attachmentId&quot;:32058698,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/4744200/Autonomous_learning_of_high_level_states_and_actions_in_continuous_environments&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/4744200/Autonomous_learning_of_high_level_states_and_actions_in_continuous_environments"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="21" data-entity-id="47788455" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/47788455/An_algebraic_approach_to_abstraction_in_reinforcement_learning">An algebraic approach to abstraction in reinforcement learning</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="67809175" href="https://independent.academia.edu/AndrewBarto">Andrew Barto</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2004</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{&quot;location&quot;:&quot;wsj-grid-card-download-pdf-modal&quot;,&quot;work_title&quot;:&quot;An algebraic approach to abstraction in reinforcement learning&quot;,&quot;attachmentId&quot;:66729633,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/47788455/An_algebraic_approach_to_abstraction_in_reinforcement_learning&quot;,&quot;alternativeTracking&quot;:true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/47788455/An_algebraic_approach_to_abstraction_in_reinforcement_learning"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div></div></div><div class="footer--content"><ul class="footer--main-links hide-on-mobile"><li><a href="https://www.academia.edu/about">About</a></li><li><a href="https://www.academia.edu/press">Press</a></li><li><a href="https://www.academia.edu/documents">Papers</a></li><li><a href="https://www.academia.edu/topics">Topics</a></li><li><a href="https://www.academia.edu/hiring"><svg style="width: 13px; height: 13px; position: relative; bottom: -1px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg>&nbsp;<strong>We&#39;re Hiring!</strong></a></li><li><a href="https://support.academia.edu/hc/en-us"><svg style="width: 12px; height: 12px; position: relative; bottom: -1px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg>&nbsp;<strong>Help Center</strong></a></li></ul><ul class="footer--research-interests"><li>Find new research papers in:</li><li><a href="https://www.academia.edu/Documents/in/Physics">Physics</a></li><li><a href="https://www.academia.edu/Documents/in/Chemistry">Chemistry</a></li><li><a href="https://www.academia.edu/Documents/in/Biology">Biology</a></li><li><a href="https://www.academia.edu/Documents/in/Health_Sciences">Health Sciences</a></li><li><a href="https://www.academia.edu/Documents/in/Ecology">Ecology</a></li><li><a href="https://www.academia.edu/Documents/in/Earth_Sciences">Earth Sciences</a></li><li><a href="https://www.academia.edu/Documents/in/Cognitive_Science">Cognitive Science</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a></li><li><a href="https://www.academia.edu/Documents/in/Computer_Science">Computer Science</a></li></ul><ul class="footer--legal-links hide-on-mobile"><li><a href="https://www.academia.edu/terms">Terms</a></li><li><a href="https://www.academia.edu/privacy">Privacy</a></li><li><a href="https://www.academia.edu/copyright">Copyright</a></li><li>Academia &copy;2025</li></ul></div> </body> </html>

Pages: 1 2 3 4 5 6 7 8 9 10