{"id":1366,"date":"2023-07-11T09:13:29","date_gmt":"2023-07-11T08:13:29","guid":{"rendered":"https:\/\/babel.isa.uma.es\/kipr\/?p=1366"},"modified":"2023-07-11T09:13:29","modified_gmt":"2023-07-11T08:13:29","slug":"approximating-the-value-function-of-rl-through-max-plus-algebra","status":"publish","type":"post","link":"https:\/\/babel.isa.uma.es\/kipr\/?p=1366","title":{"rendered":"Approximating the value function of RL through Max-Plus algebra"},"content":{"rendered":"<h4>Vinicius Mariano Gon\u00e7alves, <strong>Max-plus approximation for reinforcement learning,<\/strong> . Automatica, Volume 129, 2021 <a href=\"https:\/\/doi.org\/10.1016\/j.automatica.2021.109623\" target=\"_blank\">DOI: 10.1016\/j.automatica.2021.109623<\/a>.<\/h4>\n<blockquote><p>Max-Plus Algebra has been applied in several contexts, especially in the control of discrete events systems. In this article, we discuss another application closely related to control: the use of Max-Plus algebra concepts in the context of reinforcement learning. Max-Plus Algebra and reinforcement learning are strongly linked due to the latter\u2019s dependence on the Bellman Equation which, in some cases, is a linear Max-Plus equation. This fact motivates the application of Max-Plus algebra to approximate the value function, central to the Bellman Equation and thus also to reinforcement learning. This article proposes conditions so that this approach can be done in a simple way and following the philosophy of reinforcement learning: explore the environment, receive the rewards and use this information to improve the knowledge of the value function. The proposed conditions are related to two matrices and impose on them a relationship that is analogous to the concept of weak inverses in traditional algebra.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Vinicius Mariano Gon\u00e7alves, Max-plus approximation for reinforcement learning, . Automatica, Volume 129, 2021 DOI: 10.1016\/j.automatica.2021.109623. Max-Plus Algebra has been applied <span class=\"ellipsis\">&hellip;<\/span> <span class=\"more-link-wrap\"><a href=\"https:\/\/babel.isa.uma.es\/kipr\/?p=1366\" class=\"more-link\"><span>Read More &rarr;<\/span><\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[84],"tags":[463,15,385],"class_list":["post-1366","post","type-post","status-publish","format-standard","hentry","category-reinforcement-learning-in-ai","tag-max-plus-algebra","tag-reinforcement-learning","tag-value-function-approximation"],"_links":{"self":[{"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=\/wp\/v2\/posts\/1366"}],"collection":[{"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1366"}],"version-history":[{"count":1,"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=\/wp\/v2\/posts\/1366\/revisions"}],"predecessor-version":[{"id":1367,"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=\/wp\/v2\/posts\/1366\/revisions\/1367"}],"wp:attachment":[{"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1366"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1366"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/babel.isa.uma.es\/kipr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1366"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}