{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/f-divergence-constrained-policy-improvement","title":"f-Divergence constrained policy improvement","arxiv_id":"1801.00056","date":"2017-12-29","proceeding":null,"authors":["Boris Belousov","Jan Peters"],"abstract":"To ensure stability of learning, state-of-the-art generalized policy\niteration algorithms augment the policy improvement step with a trust region\nconstraint bounding the information loss. The size of the trust region is\ncommonly determined by the Kullback-Leibler (KL) divergence, which not only\ncaptures the notion of distance well but also yields closed-form solutions. In\nthis paper, we consider a more general class of f-divergences and derive the\ncorresponding policy update rules. The generic solution is expressed through\nthe derivative of the convex conjugate function to f and includes the KL\nsolution as a special case. Within the class of f-divergences, we further focus\non a one-parameter family of $\\alpha$-divergences to study effects of the\nchoice of divergence on policy improvement. Previously known as well as new\npolicy updates emerge for different values of $\\alpha$. We show that every type\nof policy update comes with a compatible policy evaluation resulting from the\nchosen f-divergence. Interestingly, the mean-squared Bellman error minimization\nis closely related to policy evaluation with the Pearson $\\chi^2$-divergence\npenalty, while the KL divergence results in the soft-max policy update and a\nlog-sum-exp critic. We carry out asymptotic analysis of the solutions for\ndifferent values of $\\alpha$ and demonstrate the effects of using different\ndivergence functions on a multi-armed bandit problem and on common standard\nreinforcement learning problems.","url_abs":"http://arxiv.org/abs/1801.00056v2","url_pdf":"http://arxiv.org/pdf/1801.00056v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"f-divergence-constrained-policy-improvement","repo_url":"https://github.com/hanyas/reps","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1801.00056","atlas_url":"https://app.syntology.ai/?focus=1801.00056","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}