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0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r886047488">.mw-parser-output .nobold{font-weight:normal}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886047488"><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Machine_learning" title="Machine learning">Machine learning</a><br />and <a href="/wiki/Data_mining" title="Data mining">data mining</a></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Paradigms</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Supervised_learning" title="Supervised learning">Supervised learning</a></li> <li><a href="/wiki/Unsupervised_learning" title="Unsupervised learning">Unsupervised learning</a></li> <li><a href="/wiki/Semi-supervised_learning" class="mw-redirect" title="Semi-supervised learning">Semi-supervised learning</a></li> <li><a href="/wiki/Self-supervised_learning" title="Self-supervised learning">Self-supervised learning</a></li> <li><a href="/wiki/Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a></li> <li><a href="/wiki/Meta-learning_(computer_science)" title="Meta-learning (computer science)">Meta-learning</a></li> <li><a href="/wiki/Online_machine_learning" title="Online machine learning">Online learning</a></li> <li><a href="/wiki/Batch_learning" class="mw-redirect" title="Batch learning">Batch learning</a></li> <li><a href="/wiki/Curriculum_learning" title="Curriculum learning">Curriculum learning</a></li> <li><a href="/wiki/Rule-based_machine_learning" title="Rule-based machine learning">Rule-based learning</a></li> <li><a href="/wiki/Neuro-symbolic_AI" title="Neuro-symbolic AI">Neuro-symbolic AI</a></li> <li><a href="/wiki/Neuromorphic_engineering" class="mw-redirect" title="Neuromorphic engineering">Neuromorphic engineering</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Problems</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Statistical_classification" title="Statistical classification">Classification</a></li> <li><a href="/wiki/Generative_model" title="Generative model">Generative modeling</a></li> <li><a href="/wiki/Regression_analysis" title="Regression analysis">Regression</a></li> <li><a href="/wiki/Cluster_analysis" title="Cluster analysis">Clustering</a></li> <li><a href="/wiki/Dimensionality_reduction" title="Dimensionality reduction">Dimensionality reduction</a></li> <li><a href="/wiki/Density_estimation" title="Density estimation">Density estimation</a></li> <li><a href="/wiki/Anomaly_detection" title="Anomaly detection">Anomaly detection</a></li> <li><a href="/wiki/Data_cleaning" class="mw-redirect" title="Data cleaning">Data cleaning</a></li> <li><a href="/wiki/Automated_machine_learning" title="Automated machine learning">AutoML</a></li> <li><a href="/wiki/Association_rule_learning" title="Association rule learning">Association rules</a></li> <li><a href="/wiki/Semantic_analysis_(machine_learning)" title="Semantic analysis (machine learning)">Semantic analysis</a></li> <li><a href="/wiki/Structured_prediction" title="Structured prediction">Structured prediction</a></li> <li><a href="/wiki/Feature_engineering" title="Feature engineering">Feature engineering</a></li> <li><a href="/wiki/Feature_learning" title="Feature learning">Feature learning</a></li> <li><a href="/wiki/Learning_to_rank" title="Learning to rank">Learning to rank</a></li> <li><a href="/wiki/Grammar_induction" title="Grammar induction">Grammar induction</a></li> <li><a href="/wiki/Ontology_learning" title="Ontology learning">Ontology learning</a></li> <li><a href="/wiki/Multimodal_learning" title="Multimodal learning">Multimodal learning</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Supervised_learning" title="Supervised learning">Supervised learning</a><br /><span class="nobold"><span style="font-size:85%;">(<b><a href="/wiki/Statistical_classification" title="Statistical classification">classification</a></b> • <b><a href="/wiki/Regression_analysis" title="Regression analysis">regression</a></b>)</span></span> </div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Apprenticeship_learning" title="Apprenticeship learning">Apprenticeship learning</a></li> <li><a href="/wiki/Decision_tree_learning" title="Decision tree learning">Decision trees</a></li> <li><a href="/wiki/Ensemble_learning" title="Ensemble learning">Ensembles</a> <ul><li><a href="/wiki/Bootstrap_aggregating" title="Bootstrap aggregating">Bagging</a></li> <li><a href="/wiki/Boosting_(machine_learning)" title="Boosting (machine learning)">Boosting</a></li> <li><a href="/wiki/Random_forest" title="Random forest">Random forest</a></li></ul></li> <li><a href="/wiki/K-nearest_neighbors_algorithm" title="K-nearest neighbors algorithm"><i>k</i>-NN</a></li> <li><a href="/wiki/Linear_regression" title="Linear regression">Linear regression</a></li> <li><a href="/wiki/Naive_Bayes_classifier" title="Naive Bayes classifier">Naive Bayes</a></li> <li><a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">Artificial neural networks</a></li> <li><a href="/wiki/Logistic_regression" title="Logistic regression">Logistic regression</a></li> <li><a href="/wiki/Perceptron" title="Perceptron">Perceptron</a></li> <li><a href="/wiki/Relevance_vector_machine" title="Relevance vector machine">Relevance vector machine (RVM)</a></li> <li><a href="/wiki/Support_vector_machine" title="Support vector machine">Support vector machine (SVM)</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="/wiki/Cluster_analysis" title="Cluster analysis">Clustering</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/BIRCH" title="BIRCH">BIRCH</a></li> <li><a href="/wiki/CURE_algorithm" title="CURE algorithm">CURE</a></li> <li><a href="/wiki/Hierarchical_clustering" title="Hierarchical clustering">Hierarchical</a></li> <li><a href="/wiki/K-means_clustering" title="K-means clustering"><i>k</i>-means</a></li> <li><a href="/wiki/Fuzzy_clustering" title="Fuzzy clustering">Fuzzy</a></li> <li><a href="/wiki/Expectation%E2%80%93maximization_algorithm" title="Expectation–maximization algorithm">Expectation–maximization (EM)</a></li> <li><br /><a href="/wiki/DBSCAN" title="DBSCAN">DBSCAN</a></li> <li><a href="/wiki/OPTICS_algorithm" title="OPTICS algorithm">OPTICS</a></li> <li><a href="/wiki/Mean_shift" title="Mean shift">Mean shift</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="/wiki/Dimensionality_reduction" title="Dimensionality reduction">Dimensionality reduction</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Factor_analysis" title="Factor analysis">Factor analysis</a></li> <li><a href="/wiki/Canonical_correlation" title="Canonical correlation">CCA</a></li> <li><a href="/wiki/Independent_component_analysis" title="Independent component analysis">ICA</a></li> <li><a href="/wiki/Linear_discriminant_analysis" title="Linear discriminant analysis">LDA</a></li> <li><a href="/wiki/Non-negative_matrix_factorization" title="Non-negative matrix factorization">NMF</a></li> <li><a href="/wiki/Principal_component_analysis" title="Principal component analysis">PCA</a></li> <li><a href="/wiki/Proper_generalized_decomposition" title="Proper generalized decomposition">PGD</a></li> <li><a href="/wiki/T-distributed_stochastic_neighbor_embedding" title="T-distributed stochastic neighbor embedding">t-SNE</a></li> <li><a href="/wiki/Sparse_dictionary_learning" title="Sparse dictionary learning">SDL</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="/wiki/Structured_prediction" title="Structured prediction">Structured prediction</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Graphical_model" title="Graphical model">Graphical models</a> <ul><li><a href="/wiki/Bayesian_network" title="Bayesian network">Bayes net</a></li> <li><a href="/wiki/Conditional_random_field" title="Conditional random field">Conditional random field</a></li> <li><a href="/wiki/Hidden_Markov_model" title="Hidden Markov model">Hidden Markov</a></li></ul></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="/wiki/Anomaly_detection" title="Anomaly detection">Anomaly detection</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Random_sample_consensus" title="Random sample consensus">RANSAC</a></li> <li><a href="/wiki/K-nearest_neighbors_algorithm" title="K-nearest neighbors algorithm"><i>k</i>-NN</a></li> <li><a href="/wiki/Local_outlier_factor" title="Local outlier factor">Local outlier factor</a></li> <li><a href="/wiki/Isolation_forest" title="Isolation forest">Isolation forest</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">Artificial neural network</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Autoencoder" title="Autoencoder">Autoencoder</a></li> <li><a href="/wiki/Deep_learning" title="Deep learning">Deep learning</a></li> <li><a href="/wiki/Feedforward_neural_network" title="Feedforward neural network">Feedforward neural network</a></li> <li><a href="/wiki/Recurrent_neural_network" title="Recurrent neural network">Recurrent neural network</a> <ul><li><a href="/wiki/Long_short-term_memory" title="Long short-term memory">LSTM</a></li> <li><a href="/wiki/Gated_recurrent_unit" title="Gated recurrent unit">GRU</a></li> <li><a href="/wiki/Echo_state_network" title="Echo state network">ESN</a></li> <li><a href="/wiki/Reservoir_computing" title="Reservoir computing">reservoir computing</a></li></ul></li> <li><a href="/wiki/Boltzmann_machine" title="Boltzmann machine">Boltzmann machine</a> <ul><li><a href="/wiki/Restricted_Boltzmann_machine" title="Restricted Boltzmann machine">Restricted</a></li></ul></li> <li><a href="/wiki/Generative_adversarial_network" title="Generative adversarial network">GAN</a></li> <li><a href="/wiki/Diffusion_model" title="Diffusion model">Diffusion model</a></li> <li><a href="/wiki/Self-organizing_map" title="Self-organizing map">SOM</a></li> <li><a href="/wiki/Convolutional_neural_network" title="Convolutional neural network">Convolutional neural network</a> <ul><li><a href="/wiki/U-Net" title="U-Net">U-Net</a></li> <li><a href="/wiki/LeNet" title="LeNet">LeNet</a></li> <li><a href="/wiki/AlexNet" title="AlexNet">AlexNet</a></li> <li><a href="/wiki/DeepDream" title="DeepDream">DeepDream</a></li></ul></li> <li><a href="/wiki/Neural_radiance_field" title="Neural radiance field">Neural radiance field</a></li> <li><a href="/wiki/Transformer_(machine_learning_model)" class="mw-redirect" title="Transformer (machine learning model)">Transformer</a> <ul><li><a href="/wiki/Vision_transformer" title="Vision transformer">Vision</a></li></ul></li> <li><a href="/wiki/Mamba_(deep_learning_architecture)" title="Mamba (deep learning architecture)">Mamba</a></li> <li><a href="/wiki/Spiking_neural_network" title="Spiking neural network">Spiking neural network</a></li> <li><a href="/wiki/Memtransistor" title="Memtransistor">Memtransistor</a></li> <li><a href="/wiki/Electrochemical_RAM" title="Electrochemical RAM">Electrochemical RAM</a> (ECRAM)</li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)"><a href="/wiki/Reinforcement_learning" title="Reinforcement learning">Reinforcement learning</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Q-learning" title="Q-learning">Q-learning</a></li> <li><a href="/wiki/State%E2%80%93action%E2%80%93reward%E2%80%93state%E2%80%93action" title="State–action–reward–state–action">SARSA</a></li> <li><a href="/wiki/Temporal_difference_learning" title="Temporal difference learning">Temporal difference (TD)</a></li> <li><a class="mw-selflink selflink">Multi-agent</a> <ul><li><a href="/wiki/Self-play_(reinforcement_learning_technique)" class="mw-redirect" title="Self-play (reinforcement learning technique)">Self-play</a></li></ul></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Learning with humans</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Active_learning_(machine_learning)" title="Active learning (machine learning)">Active learning</a></li> <li><a href="/wiki/Crowdsourcing" title="Crowdsourcing">Crowdsourcing</a></li> <li><a href="/wiki/Human-in-the-loop" title="Human-in-the-loop">Human-in-the-loop</a></li> <li><a href="/wiki/Reinforcement_learning_from_human_feedback" title="Reinforcement learning from human feedback">RLHF</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Model diagnostics</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Coefficient_of_determination" title="Coefficient of determination">Coefficient of determination</a></li> <li><a href="/wiki/Confusion_matrix" title="Confusion matrix">Confusion matrix</a></li> <li><a href="/wiki/Learning_curve_(machine_learning)" title="Learning curve (machine learning)">Learning curve</a></li> <li><a href="/wiki/Receiver_operating_characteristic" title="Receiver operating characteristic">ROC curve</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Mathematical foundations</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Kernel_machines" class="mw-redirect" title="Kernel machines">Kernel machines</a></li> <li><a href="/wiki/Bias%E2%80%93variance_tradeoff" title="Bias–variance tradeoff">Bias–variance tradeoff</a></li> <li><a href="/wiki/Computational_learning_theory" title="Computational learning theory">Computational learning theory</a></li> <li><a href="/wiki/Empirical_risk_minimization" title="Empirical risk minimization">Empirical risk minimization</a></li> <li><a href="/wiki/Occam_learning" title="Occam learning">Occam learning</a></li> <li><a href="/wiki/Probably_approximately_correct_learning" title="Probably approximately correct learning">PAC learning</a></li> <li><a href="/wiki/Statistical_learning_theory" title="Statistical learning theory">Statistical learning</a></li> <li><a href="/wiki/Vapnik%E2%80%93Chervonenkis_theory" title="Vapnik–Chervonenkis theory">VC theory</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Journals and conferences</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/ECML_PKDD" title="ECML PKDD">ECML PKDD</a></li> <li><a href="/wiki/Conference_on_Neural_Information_Processing_Systems" title="Conference on Neural Information Processing Systems">NeurIPS</a></li> <li><a href="/wiki/International_Conference_on_Machine_Learning" title="International Conference on Machine Learning">ICML</a></li> <li><a href="/wiki/International_Conference_on_Learning_Representations" title="International Conference on Learning Representations">ICLR</a></li> <li><a href="/wiki/International_Joint_Conference_on_Artificial_Intelligence" title="International Joint Conference on Artificial Intelligence">IJCAI</a></li> <li><a href="/wiki/Machine_Learning_(journal)" title="Machine Learning (journal)">ML</a></li> <li><a href="/wiki/Journal_of_Machine_Learning_Research" title="Journal of Machine Learning Research">JMLR</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed machine-learning-list-title"><div class="sidebar-list-title" style="border-top:1px solid #aaa; text-align:center;;color: var(--color-base)">Related articles</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Glossary_of_artificial_intelligence" title="Glossary of artificial intelligence">Glossary of artificial intelligence</a></li> <li><a href="/wiki/List_of_datasets_for_machine-learning_research" title="List of datasets for machine-learning research">List of datasets for machine-learning research</a> <ul><li><a href="/wiki/List_of_datasets_in_computer_vision_and_image_processing" title="List of datasets in computer vision and image processing">List of datasets in computer vision and image processing</a></li></ul></li> <li><a href="/wiki/Outline_of_machine_learning" title="Outline of machine learning">Outline of machine learning</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Machine_learning" title="Template:Machine learning"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Machine_learning" title="Template talk:Machine learning"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Machine_learning" title="Special:EditPage/Template:Machine learning"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Magent-graph-2.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Magent-graph-2.gif/220px-Magent-graph-2.gif" decoding="async" width="220" height="197" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Magent-graph-2.gif/330px-Magent-graph-2.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/Magent-graph-2.gif/440px-Magent-graph-2.gif 2x" data-file-width="500" data-file-height="448" /></a><figcaption>Two rival teams of agents face off in a <a rel="nofollow" class="external text" href="https://github.com/Farama-Foundation/MAgent#readme">MARL experiment</a></figcaption></figure> <p><b>Multi-agent reinforcement learning (MARL)</b> is a sub-field of <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">reinforcement learning</a>. It focuses on studying the behavior of multiple learning agents that coexist in a shared environment.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Each agent is motivated by its own rewards, and does actions to advance its own interests; in some environments these interests are opposed to the interests of other agents, resulting in complex <a href="/wiki/Group_dynamics" title="Group dynamics">group dynamics</a>. </p><p>Multi-agent reinforcement learning is closely related to <a href="/wiki/Game_theory" title="Game theory">game theory</a> and especially <a href="/wiki/Repeated_game" title="Repeated game">repeated games</a>, as well as <a href="/wiki/Multi-agent_system" title="Multi-agent system">multi-agent systems</a>. Its study combines the pursuit of finding ideal algorithms that maximize rewards with a more sociological set of concepts. While research in single-agent reinforcement learning is concerned with finding the algorithm that gets the biggest number of points for one agent, research in multi-agent reinforcement learning evaluates and quantifies social metrics, such as cooperation,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> reciprocity,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> equity,<sup id="cite_ref-Hughes_2018_inequity_4-0" class="reference"><a href="#cite_note-Hughes_2018_inequity-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> social influence,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> language<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> and discrimination.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Similarly to <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">single-agent reinforcement learning</a>, multi-agent reinforcement learning is modeled as some form of a <a href="/wiki/Markov_decision_process" title="Markov decision process">Markov decision process (MDP)</a>. For example, </p> <ul><li>A set <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> of environment states.</li> <li>One set <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {A}}_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">A</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {A}}_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a237e3831acdc4229ee8a60fb4d4d764a34567" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.654ex; height:2.676ex;" alt="{\displaystyle {\mathcal {A}}_{i}}"></span> of actions for each of the agents <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\in I=\{1,...,N\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>N</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\in I=\{1,...,N\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2a423aef18e8a09dd3b6cef256a520b74b9f492" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.634ex; height:2.843ex;" alt="{\displaystyle i\in I=\{1,...,N\}}"></span>.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{\overrightarrow {a}}(s,s')=\Pr(s_{t+1}=s'\mid s_{t}=s,{\overrightarrow {a}}_{t}={\overrightarrow {a}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>→</mo> </mover> </mrow> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo>,</mo> <msup> <mi>s</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msup> <mi>s</mi> <mo>′</mo> </msup> <mo>∣</mo> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>s</mi> <mo>,</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>→</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>→</mo> </mover> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\overrightarrow {a}}(s,s')=\Pr(s_{t+1}=s'\mid s_{t}=s,{\overrightarrow {a}}_{t}={\overrightarrow {a}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/839e48885b6f207ea40b02e7961007ef42b3c775" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:43.018ex; height:4.176ex;" alt="{\displaystyle P_{\overrightarrow {a}}(s,s')=\Pr(s_{t+1}=s'\mid s_{t}=s,{\overrightarrow {a}}_{t}={\overrightarrow {a}})}"></span> is the probability of transition (at time <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>) from state <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> to state <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>s</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5136680c63706cfd17ceddb4acddbfdd0ba5ef2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.775ex; height:2.509ex;" alt="{\displaystyle s'}"></span> under joint action <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>→</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b77149adfb778a5de4e0f9e99243919227669a7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:3.009ex;" alt="{\displaystyle {\overrightarrow {a}}}"></span>.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {R}}_{\overrightarrow {a}}(s,s')}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>R</mi> <mo>→</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>→</mo> </mover> </mrow> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo>,</mo> <msup> <mi>s</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {R}}_{\overrightarrow {a}}(s,s')}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3584e0cc06964854858067b74b720f7884223189" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:10.101ex; height:4.843ex;" alt="{\displaystyle {\overrightarrow {R}}_{\overrightarrow {a}}(s,s')}"></span> is the immediate joint reward after the transition from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>s</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5136680c63706cfd17ceddb4acddbfdd0ba5ef2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.775ex; height:2.509ex;" alt="{\displaystyle s'}"></span> with joint action <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overrightarrow {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo>→</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overrightarrow {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b77149adfb778a5de4e0f9e99243919227669a7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:3.009ex;" alt="{\displaystyle {\overrightarrow {a}}}"></span>.</li></ul> <p>In settings with <a href="/wiki/Perfect_information" title="Perfect information">perfect information</a>, such as the games of <a href="/wiki/Chess" title="Chess">chess</a> and <a href="/wiki/Go_(game)" title="Go (game)">Go</a>, the MDP would be fully observable. In settings with imperfect information, especially in real-world applications like <a href="/wiki/Self-driving_car" title="Self-driving car">self-driving cars</a>, each agent would access an observation that only has part of the information about the current state. In the partially observable setting, the core model is the partially observable <a href="/wiki/Stochastic_game" title="Stochastic game">stochastic game</a> in the general case, and the <a href="/wiki/Decentralized_partially_observable_Markov_decision_process" title="Decentralized partially observable Markov decision process">decentralized POMDP</a> in the cooperative case. </p> <div class="mw-heading mw-heading2"><h2 id="Cooperation_vs._competition">Cooperation vs. competition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=2" title="Edit section: Cooperation vs. competition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When multiple agents are acting in a shared environment their interests might be aligned or misaligned. MARL allows exploring all the different alignments and how they affect the agents' behavior: </p> <ul><li>In <a href="#Pure_competition_settings">pure competition settings</a>, the agents' rewards are exactly opposite to each other, and therefore they are playing <i>against</i> each other.</li> <li><a href="#Pure_cooperation_settings">Pure cooperation settings</a> are the other extreme, in which agents get the exact same rewards, and therefore they are playing <i>with</i> each other.</li> <li><a href="#Mixed-sum_settings">Mixed-sum settings</a> cover all the games that combine elements of both cooperation and competition.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Pure_competition_settings">Pure competition settings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=3" title="Edit section: Pure competition settings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When two agents are playing a <a href="/wiki/Zero-sum_game" title="Zero-sum game">zero-sum game</a>, they are in pure competition with each other. Many traditional games such as <a href="/wiki/Chess" title="Chess">chess</a> and <a href="/wiki/Go_(game)" title="Go (game)">Go</a> fall under this category, as do two-player variants of modern games like <a href="/wiki/StarCraft" title="StarCraft">StarCraft</a>. Because each agent can only win at the expense of the other agent, many complexities are stripped away. There's no prospect of communication or social dilemmas, as neither agent is incentivized to take actions that benefit its opponent. </p><p>The <a href="/wiki/Deep_Blue_(chess_computer)" title="Deep Blue (chess computer)">Deep Blue</a><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/AlphaGo" title="AlphaGo">AlphaGo</a> projects demonstrate how to optimize the performance of agents in pure competition settings. </p><p>One complexity that is not stripped away in pure competition settings is <a href="#Autocurricula">autocurricula</a>. As the agents' policy is improved using <a href="/wiki/Self-play_(reinforcement_learning_technique)" class="mw-redirect" title="Self-play (reinforcement learning technique)">self-play</a>, multiple layers of learning may occur. </p> <div class="mw-heading mw-heading3"><h3 id="Pure_cooperation_settings">Pure cooperation settings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=4" title="Edit section: Pure cooperation settings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>MARL is used to explore how separate agents with identical interests can communicate and work together. Pure cooperation settings are explored in recreational <a href="/wiki/Cooperative_video_game" title="Cooperative video game">cooperative games</a> such as <a href="/wiki/Overcooked" title="Overcooked">Overcooked</a>,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> as well as real-world scenarios in <a href="/wiki/Robotics" title="Robotics">robotics</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>In pure cooperation settings all the agents get identical rewards, which means that social dilemmas do not occur. </p><p>In pure cooperation settings, oftentimes there are an arbitrary number of coordination strategies, and agents converge to specific "conventions" when coordinating with each other. The notion of conventions has been studied in language<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> and also alluded to in more general multi-agent collaborative tasks.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Mixed-sum_settings">Mixed-sum settings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=5" title="Edit section: Mixed-sum settings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Multi_give_way_(4_agents,_each_trying_to_reach_a_specific_point).gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Multi_give_way_%284_agents%2C_each_trying_to_reach_a_specific_point%29.gif/220px-Multi_give_way_%284_agents%2C_each_trying_to_reach_a_specific_point%29.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/Multi_give_way_%284_agents%2C_each_trying_to_reach_a_specific_point%29.gif/330px-Multi_give_way_%284_agents%2C_each_trying_to_reach_a_specific_point%29.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/Multi_give_way_%284_agents%2C_each_trying_to_reach_a_specific_point%29.gif/440px-Multi_give_way_%284_agents%2C_each_trying_to_reach_a_specific_point%29.gif 2x" data-file-width="450" data-file-height="450" /></a><figcaption>In this mixed sum setting, each of the four agents is trying to reach a different goal. Each agent's success depends on the other agents clearing its way, even though they are not directly incentivized to assist each other.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>Most real-world scenarios involving multiple agents have elements of both cooperation and competition. For example, when multiple <a href="/wiki/Self-driving_cars" class="mw-redirect" title="Self-driving cars">self-driving cars</a> are planning their respective paths, each of them has interests that are diverging but not exclusive: Each car is minimizing the amount of time it's taking to reach its destination, but all cars have the shared interest of avoiding a <a href="/wiki/Traffic_collision" title="Traffic collision">traffic collision</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>Zero-sum settings with three or more agents often exhibit similar properties to mixed-sum settings, since each pair of agents might have a non-zero utility sum between them. </p><p>Mixed-sum settings can be explored using classic <a href="/wiki/Normal-form_game" title="Normal-form game">matrix games</a> such as <a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">prisoner's dilemma</a>, more complex <a href="#Sequential_social_dilemmas">sequential social dilemmas</a>, and recreational games such as <a href="/wiki/Among_Us" title="Among Us">Among Us</a>,<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Diplomacy_(game)" title="Diplomacy (game)">Diplomacy</a><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/StarCraft_II" title="StarCraft II">StarCraft II</a>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>Mixed-sum settings can give rise to communication and social dilemmas. </p> <div class="mw-heading mw-heading2"><h2 id="Social_dilemmas">Social dilemmas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=6" title="Edit section: Social dilemmas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As in <a href="/wiki/Game_theory" title="Game theory">game theory</a>, much of the research in MARL revolves around <a href="/wiki/Collective_action_problem" title="Collective action problem">social dilemmas</a>, such as <a href="/wiki/Prisoner%27s_dilemma" title="Prisoner's dilemma">prisoner's dilemma</a>,<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Chicken_(game)" title="Chicken (game)">chicken</a> and <a href="/wiki/Stag_hunt" title="Stag hunt">stag hunt</a>.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>While game theory research might focus on <a href="/wiki/Nash_equilibrium" title="Nash equilibrium">Nash equilibria</a> and what an ideal policy for an agent would be, MARL research focuses on how the agents would learn these ideal policies using a trial-and-error process. The <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">reinforcement learning</a> algorithms that are used to train the agents are maximizing the agent's own reward; the conflict between the needs of the agents and the needs of the group is a subject of active research.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>Various techniques have been explored in order to induce cooperation in agents: Modifying the environment rules,<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> adding intrinsic rewards,<sup id="cite_ref-Hughes_2018_inequity_4-1" class="reference"><a href="#cite_note-Hughes_2018_inequity-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and more. </p> <div class="mw-heading mw-heading3"><h3 id="Sequential_social_dilemmas">Sequential social dilemmas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=7" title="Edit section: Sequential social dilemmas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Social dilemmas like prisoner's dilemma, chicken and stag hunt are "matrix games". Each agent takes only one action from a choice of two possible actions, and a simple 2x2 matrix is used to describe the reward that each agent will get, given the actions that each agent took. </p><p>In humans and other living creatures, social dilemmas tend to be more complex. Agents take multiple actions over time, and the distinction between cooperating and defecting is not as clear cut as in matrix games. The concept of a <b>sequential social dilemma (SSD)</b> was introduced in 2017<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> as an attempt to model that complexity. There is ongoing research into defining different kinds of SSDs and showing cooperative behavior in the agents that act in them.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Autocurricula">Autocurricula</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=8" title="Edit section: Autocurricula"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An autocurriculum<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> (plural: autocurricula) is a reinforcement learning concept that's salient in multi-agent experiments. As agents improve their performance, they change their environment; this change in the environment affects themselves and the other agents. The feedback loop results in several distinct phases of learning, each depending on the previous one. The stacked layers of learning are called an autocurriculum. Autocurricula are especially apparent in adversarial settings,<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> where each group of agents is racing to counter the current strategy of the opposing group. </p><p>The <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=kopoLzvh5jY">Hide and Seek game</a> is an accessible example of an autocurriculum occurring in an adversarial setting. In this experiment, a team of seekers is competing against a team of hiders. Whenever one of the teams learns a new strategy, the opposing team adapts its strategy to give the best possible counter. When the hiders learn to use boxes to build a shelter, the seekers respond by learning to use a ramp to break into that shelter. The hiders respond by locking the ramps, making them unavailable for the seekers to use. The seekers then respond by "box surfing", exploiting a <a href="/wiki/Glitching" class="mw-redirect" title="Glitching">glitch</a> in the game to penetrate the shelter. Each "level" of learning is an emergent phenomenon, with the previous level as its premise. This results in a stack of behaviors, each dependent on its predecessor. </p><p>Autocurricula in reinforcement learning experiments are compared to the stages of the <a href="/wiki/Evolution" title="Evolution">evolution of life on Earth</a> and the development of <a href="/wiki/Culture" title="Culture">human culture</a>. A major stage in evolution happened 2-3 billion years ago, when <a href="/wiki/Photosynthesis" title="Photosynthesis">photosynthesizing life forms</a> started to produce massive amounts of <a href="/wiki/Oxygen" title="Oxygen">oxygen</a>, changing the balance of gases in the atmosphere.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> In the next stages of evolution, oxygen-breathing life forms evolved, eventually leading up to land <a href="/wiki/Mammal" title="Mammal">mammals</a> and human beings. These later stages could only happen after the photosynthesis stage made oxygen widely available. Similarly, human culture could not have gone through the <a href="/wiki/Industrial_Revolution" title="Industrial Revolution">Industrial Revolution</a> in the 18th century without the resources and insights gained by the <a href="/wiki/Neolithic_Revolution" title="Neolithic Revolution">agricultural revolution</a> at around 10,000 BC.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=9" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Multi-agent reinforcement learning has been applied to a variety of use cases in science and industry: </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 18em;"> <ul><li><a href="/wiki/Broadband" title="Broadband">Broadband</a> <a href="/wiki/Cellular_networks" class="mw-redirect" title="Cellular networks">cellular networks</a> such as <a href="/wiki/5G" title="5G">5G</a><sup id="cite_ref-Li_2022_32-0" class="reference"><a href="#cite_note-Li_2022-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Cache_(computing)" title="Cache (computing)">Content caching</a><sup id="cite_ref-Li_2022_32-1" class="reference"><a href="#cite_note-Li_2022-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Routing" title="Routing">Packet routing</a><sup id="cite_ref-Li_2022_32-2" class="reference"><a href="#cite_note-Li_2022-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Computer_vision" title="Computer vision">Computer vision</a><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Network_security" title="Network security">Network security</a><sup id="cite_ref-Li_2022_32-3" class="reference"><a href="#cite_note-Li_2022-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Power_control#Transmit_power_control" title="Power control">Transmit power control</a><sup id="cite_ref-Li_2022_32-4" class="reference"><a href="#cite_note-Li_2022-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Computation_offloading" title="Computation offloading">Computation offloading</a><sup id="cite_ref-Li_2022_32-5" class="reference"><a href="#cite_note-Li_2022-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Evolution_of_languages" title="Evolution of languages">Language evolution research</a><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Global_health" title="Global health">Global health</a><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Integrated_circuit_design" title="Integrated circuit design">Integrated circuit design</a><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Internet_of_Things" class="mw-redirect" title="Internet of Things">Internet of Things</a><sup id="cite_ref-Li_2022_32-6" class="reference"><a href="#cite_note-Li_2022-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Microgrid" title="Microgrid">Microgrid</a> <a href="/wiki/Energy_management" title="Energy management">energy management</a><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup></li> <li>Multi-camera control<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Self-driving_car" title="Self-driving car">Autonomous vehicles</a><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Sports_analytics" title="Sports analytics">Sports analytics</a><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Traffic_control" class="mw-redirect" title="Traffic control">Traffic control</a><sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> (<a href="/wiki/Ramp_metering" class="mw-redirect" title="Ramp metering">Ramp metering</a><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup>)</li> <li><a href="/wiki/Unmanned_aerial_vehicles" class="mw-redirect" title="Unmanned aerial vehicles">Unmanned aerial vehicles</a><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Li_2022_32-7" class="reference"><a href="#cite_note-Li_2022-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Wildlife_conservation" title="Wildlife conservation">Wildlife conservation</a><sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup></li></ul></div> <div class="mw-heading mw-heading3"><h3 id="AI_alignment">AI alignment</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=10" title="Edit section: AI alignment"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Multi-agent reinforcement learning has been used in research into <a href="/wiki/AI_alignment" title="AI alignment">AI alignment</a>. The relationship between the different agents in a MARL setting can be compared to the relationship between a human and an AI agent. Research efforts in the intersection of these two fields attempt to simulate possible conflicts between a human's intentions and an AI agent's actions, and then explore which variables could be changed to prevent these conflicts.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Limitations">Limitations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=11" title="Edit section: Limitations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are some inherent difficulties about multi-agent <a href="/wiki/Deep_reinforcement_learning" title="Deep reinforcement learning">deep reinforcement learning</a>.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> The environment is not stationary anymore, thus the <a href="/wiki/Markov_property" title="Markov property">Markov property</a> is violated: transitions and rewards do not only depend on the current state of an agent. </p> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multi-agent_reinforcement_learning&action=edit&section=12" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box metadata side-box-right"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Scholia_logo.svg/40px-Scholia_logo.svg.png" decoding="async" width="40" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Scholia_logo.svg/60px-Scholia_logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Scholia_logo.svg/80px-Scholia_logo.svg.png 2x" data-file-width="107" data-file-height="104" /></span></span></div> <div class="side-box-text plainlist"><a href="https://www.wikidata.org/wiki/Wikidata:Scholia" class="extiw" title="d:Wikidata:Scholia">Scholia</a> has a <i>topic</i> profile for <i><b><a href="https://iw.toolforge.org/scholia/topic/Q85786957" class="extiw" title="toolforge:scholia/topic/Q85786957">Multi-agent reinforcement learning</a></b></i>.</div></div> </div> <ul><li>Stefano V. 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