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(PDF) HEBO: An Empirical Study of Assumptions in Bayesian Optimisation | alexandre maraval - Academia.edu

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Our results on the Bayesmark benchmark indicate that heteroscedasticity and non-stationarity pose significant challenges for black-box" /> <meta property="article:author" content="https://independent.academia.edu/alexandremaraval" /> <meta name="description" content="In this work we rigorously analyse assumptions inherent to black-box optimisation hyper-parameter tuning tasks. Our results on the Bayesmark benchmark indicate that heteroscedasticity and non-stationarity pose significant challenges for black-box" /> <title>(PDF) HEBO: An Empirical Study of Assumptions in Bayesian Optimisation | alexandre maraval - Academia.edu</title> <link rel="canonical" href="https://www.academia.edu/113649420/HEBO_An_Empirical_Study_of_Assumptions_in_Bayesian_Optimisation" /> <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 = 'c7ac46e400875c3b13c788ad246730fe5f6b36cc'; 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(1732753458000); window.Aedu.timeDifference = new Date().getTime() - 1732753458000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"In this work we rigorously analyse assumptions inherent to black-box optimisation hyper-parameter tuning tasks. Our results on the Bayesmark benchmark indicate that heteroscedasticity and non-stationarity pose significant challenges for black-box optimisers. Based on these findings, we propose a Heteroscedastic and Evolutionary Bayesian Optimisation solver (HEBO). HEBO performs non-linear input and output warping, admits exact marginal log-likelihood optimisation and is robust to the values of learned parameters. We demonstrate HEBO’s empirical efficacy on the NeurIPS 2020 Black-Box Optimisation challenge, where HEBO placed first. Upon further analysis, we observe that HEBO significantly outperforms existing black-box optimisers on 108 machine learning hyperparameter tuning tasks comprising the Bayesmark benchmark. Our findings indicate that the majority of hyper-parameter tuning tasks exhibit heteroscedasticity and non-stationarity, multiobjective acquisition ensembles with Pareto ...","author":[{"@context":"https://schema.org","@type":"Person","name":"alexandre maraval"}],"contributor":[],"dateCreated":"2024-01-17","dateModified":"2024-01-17","datePublished":null,"headline":"HEBO: An Empirical Study of Assumptions in Bayesian Optimisation","inLanguage":"en","keywords":["Cognitive Science","Applied Mathematics","Computer Science","Artificial Intelligence","Machine Learning","Heteroscedasticity","Bayesian Optimization","Black Box","Bayesian Probability","Hyperparameter Optimization"],"locationCreated":null,"publication":"Journal of Artificial Intelligence Research","publisher":{"@context":"https://schema.org","@type":"Organization","name":"AI Access Foundation"},"image":null,"thumbnailUrl":null,"url":"https://www.academia.edu/113649420/HEBO_An_Empirical_Study_of_Assumptions_in_Bayesian_Optimisation","sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":null}]}</script><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/single_work_page/loswp-102fa537001ba4d8dcd921ad9bd56c474abc201906ea4843e7e7efe9dfbf561d.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/body-8d679e925718b5e8e4b18e9a4fab37f7eaa99e43386459376559080ac8f2856a.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/button-3cea6e0ad4715ed965c49bfb15dedfc632787b32ff6d8c3a474182b231146ab7.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/text_button-73590134e40cdb49f9abdc8e796cc00dc362693f3f0f6137d6cf9bb78c318ce7.css" /><link crossorigin="" href="https://fonts.gstatic.com/" 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Our results on the Bayesmark benchmark indicate that heteroscedasticity and non-stationarity pose significant challenges for black-box optimisers. Based on these findings, we propose a Heteroscedastic and Evolutionary Bayesian Optimisation solver (HEBO). HEBO performs non-linear input and output warping, admits exact marginal log-likelihood optimisation and is robust to the values of learned parameters. We demonstrate HEBO’s empirical efficacy on the NeurIPS 2020 Black-Box Optimisation challenge, where HEBO placed first. Upon further analysis, we observe that HEBO significantly outperforms existing black-box optimisers on 108 machine learning hyperparameter tuning tasks comprising the Bayesmark benchmark. Our findings indicate that the majority of hyper-parameter tuning tasks exhibit heteroscedasticity and non-stationarity, multiobjective acquisition ensembles with Pareto ...","publisher":"AI Access Foundation","publication_name":"Journal of Artificial Intelligence Research"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"HEBO: An Empirical Study of Assumptions in Bayesian Optimisation","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [67755877]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</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;:110554726,&quot;attachmentType&quot;:&quot;pdf&quot;}"><img alt="First page of “HEBO: An Empirical Study of Assumptions in Bayesian Optimisation”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/110554726/mini_magick20240117-1-ic777d.png?1705518304" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.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">HEBO: An Empirical Study of Assumptions in Bayesian Optimisation</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="67755877" href="https://independent.academia.edu/alexandremaraval"><img alt="Profile image of alexandre maraval" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />alexandre maraval</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">Journal of Artificial Intelligence Research</p></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">In this work we rigorously analyse assumptions inherent to black-box optimisation hyper-parameter tuning tasks. Our results on the Bayesmark benchmark indicate that heteroscedasticity and non-stationarity pose significant challenges for black-box optimisers. Based on these findings, we propose a Heteroscedastic and Evolutionary Bayesian Optimisation solver (HEBO). HEBO performs non-linear input and output warping, admits exact marginal log-likelihood optimisation and is robust to the values of learned parameters. We demonstrate HEBO’s empirical efficacy on the NeurIPS 2020 Black-Box Optimisation challenge, where HEBO placed first. Upon further analysis, we observe that HEBO significantly outperforms existing black-box optimisers on 108 machine learning hyperparameter tuning tasks comprising the Bayesmark benchmark. Our findings indicate that the majority of hyper-parameter tuning tasks exhibit heteroscedasticity and non-stationarity, multiobjective acquisition ensembles with Pareto ...</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;:110554726,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:&quot;https://www.academia.edu/113649420/HEBO_An_Empirical_Study_of_Assumptions_in_Bayesian_Optimisation&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;:110554726,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;workUrl&quot;:&quot;https://www.academia.edu/113649420/HEBO_An_Empirical_Study_of_Assumptions_in_Bayesian_Optimisation&quot;}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="110554726" data-landing_url="https://www.academia.edu/113649420/HEBO_An_Empirical_Study_of_Assumptions_in_Bayesian_Optimisation" 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="113649422" 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/113649422/HEBO_Pushing_The_Limits_of_Sample_Efficient_Hyperparameter_Optimisation">HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation</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="67755877" href="https://independent.academia.edu/alexandremaraval">alexandre maraval</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 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;HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation&quot;,&quot;attachmentId&quot;:110554729,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/113649422/HEBO_Pushing_The_Limits_of_Sample_Efficient_Hyperparameter_Optimisation&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/113649422/HEBO_Pushing_The_Limits_of_Sample_Efficient_Hyperparameter_Optimisation"><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="113649419" 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/113649419/An_Empirical_Study_of_Assumptions_in_Bayesian_Optimisation">An Empirical Study of Assumptions in Bayesian Optimisation</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="67755877" href="https://independent.academia.edu/alexandremaraval">alexandre maraval</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2020</p><p class="ds-related-work--abstract ds2-5-body-sm">In this work we rigorously analyse assumptions inherent to black-box optimisation hyper-parameter tuning tasks. 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We show that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization for many algorithms including latent Dirichlet allocation, structured SVMs and convolutional neural networks.</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;Practical Bayesian Optimization of Machine Learning Algorithms&quot;,&quot;attachmentId&quot;:47247998,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/26986691/Practical_Bayesian_Optimization_of_Machine_Learning_Algorithms&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/26986691/Practical_Bayesian_Optimization_of_Machine_Learning_Algorithms"><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="81408586" 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/81408586/Sherpa_Hyperparameter_Optimization_for_Machine_Learning_Models">Sherpa: Hyperparameter Optimization for Machine Learning Models</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="39569978" href="https://uci.academia.edu/PeterSadowski">Peter Sadowski</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2018</p><p class="ds-related-work--abstract ds2-5-body-sm">Sherpa is a free open-source hyperparameter optimization library for machine learning models. It is designed for problems with computationally expensive iterative function evaluations, such as the hyperparameter tuning of deep neural networks. With Sherpa, scientists can quickly optimize hyperparameters using a variety of powerful and interchangeable algorithms. Additionally, the framework makes it easy to implement custom algorithms. Sherpa can be run on either a single machine or a cluster via a grid scheduler with minimal configuration. Finally, an interactive dashboard enables users to view the progress of models as they are trained, cancel trials, and explore which hyperparameter combinations are working best. Sherpa empowers machine learning researchers by automating the tedious aspects of model tuning and providing an extensible framework for developing automated hyperparameter-tuning strategies. Its source code and documentation are available at https://github.com/LarsHH/she...</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;Sherpa: Hyperparameter Optimization for Machine Learning Models&quot;,&quot;attachmentId&quot;:87461222,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/81408586/Sherpa_Hyperparameter_Optimization_for_Machine_Learning_Models&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/81408586/Sherpa_Hyperparameter_Optimization_for_Machine_Learning_Models"><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="90032062" 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/90032062/Lifelong_Bayesian_Optimization">Lifelong Bayesian Optimization</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="243800885" href="https://independent.academia.edu/ahmedalaa472">ahmed alaa</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2019</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;Lifelong Bayesian Optimization&quot;,&quot;attachmentId&quot;:93707917,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/90032062/Lifelong_Bayesian_Optimization&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/90032062/Lifelong_Bayesian_Optimization"><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="108991398" 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/108991398/Bayesian_Optimization_for_Selecting_Efficient_Machine_Learning_Models">Bayesian Optimization for Selecting Efficient Machine Learning Models</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="31060757" href="https://independent.academia.edu/TrungHBui">Trung H. Bui</a></div><p class="ds-related-work--metadata ds2-5-body-xs">ArXiv, 2020</p><p class="ds-related-work--abstract ds2-5-body-sm">The performance of many machine learning models depends on their hyper-parameter settings. Bayesian Optimization has become a successful tool for hyper-parameter optimization of machine learning algorithms, which aims to identify optimal hyper-parameters during an iterative sequential process. However, most of the Bayesian Optimization algorithms are designed to select models for effectiveness only and ignore the important issue of model training efficiency. Given that both model effectiveness and training time are important for real-world applications, models selected for effectiveness may not meet the strict training time requirements necessary to deploy in a production environment. In this work, we present a unified Bayesian Optimization framework for jointly optimizing models for both prediction effectiveness and training efficiency. We propose an objective that captures the tradeoff between these two metrics and demonstrate how we can jointly optimize them in a principled Bayes...</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;Bayesian Optimization for Selecting Efficient Machine Learning Models&quot;,&quot;attachmentId&quot;:107239828,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/108991398/Bayesian_Optimization_for_Selecting_Efficient_Machine_Learning_Models&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/108991398/Bayesian_Optimization_for_Selecting_Efficient_Machine_Learning_Models"><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="71104432" 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/71104432/Pareto_efficient_Acquisition_Functions_for_Cost_Aware_Bayesian_Optimization">Pareto-efficient Acquisition Functions for Cost-Aware Bayesian Optimization</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="160417551" href="https://mit.academia.edu/gauthierguinet">gauthier guinet</a></div><p class="ds-related-work--metadata ds2-5-body-xs">ArXiv, 2020</p><p class="ds-related-work--abstract ds2-5-body-sm">Bayesian optimization (BO) is a popular method to optimize expensive black-box functions. It efficiently tunes machine learning algorithms under the implicit assumption that hyperparameter evaluations cost approximately the same. In reality, the cost of evaluating different hyperparameters, be it in terms of time, dollars or energy, can span several orders of magnitude of difference. While a number of heuristics have been proposed to make BO cost-aware, none of these have been proven to work robustly. In this work, we reformulate cost-aware BO in terms of Pareto efficiency and introduce the cost Pareto Front, a mathematical object allowing us to highlight the shortcomings of commonly used acquisition functions. Based on this, we propose a novel Pareto-efficient adaptation of the expected improvement. On 144 real-world black-box function optimization problems we show that our Pareto-efficient acquisition functions significantly outperform previous solutions, bringing up to 50% speed-...</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;Pareto-efficient Acquisition Functions for Cost-Aware Bayesian Optimization&quot;,&quot;attachmentId&quot;:80597192,&quot;attachmentType&quot;:&quot;pdf&quot;,&quot;work_url&quot;:&quot;https://www.academia.edu/71104432/Pareto_efficient_Acquisition_Functions_for_Cost_Aware_Bayesian_Optimization&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/71104432/Pareto_efficient_Acquisition_Functions_for_Cost_Aware_Bayesian_Optimization"><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;:110554726,&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;:110554726,&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_110554726" 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. 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