{"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/near-optimal-policy-identification-in-robust","title":"Near-Optimal Policy Identification in Robust Constrained Markov Decision Processes via Epigraph Form","arxiv_id":"2408.16286","date":"2024-08-29","proceeding":null,"authors":["Toshinori Kitamura","Tadashi Kozuno","Wataru Kumagai","Kenta Hoshino","Yohei Hosoe","Kazumi Kasaura","Masashi Hamaya","Paavo Parmas","Yutaka Matsuo"],"abstract":"Designing a safe policy for uncertain environments is crucial in real-world control systems. However, this challenge remains inadequately addressed within the Markov decision process (MDP) framework. This paper presents the first algorithm guaranteed to identify a near-optimal policy in a robust constrained MDP (RCMDP), where an optimal policy minimizes cumulative cost while satisfying constraints in the worst-case scenario across a set of environments. We first prove that the conventional policy gradient approach to the Lagrangian max-min formulation can become trapped in suboptimal solutions. This occurs when its inner minimization encounters a sum of conflicting gradients from the objective and constraint functions. To address this, we leverage the epigraph form of the RCMDP problem, which resolves the conflict by selecting a single gradient from either the objective or the constraints. Building on the epigraph form, we propose a bisection search algorithm with a policy gradient subroutine and prove that it identifies an $\\varepsilon$-optimal policy in an RCMDP with $\\tilde{\\mathcal{O}}(\\varepsilon^{-4})$ robust policy evaluations.","url_abs":"https://arxiv.org/abs/2408.16286v4","url_pdf":"https://arxiv.org/pdf/2408.16286v4.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":"near-optimal-policy-identification-in-robust","repo_url":"https://github.com/matsuolab/rcmdp-epigraph","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[{"task_slug":"form","task_name":"Form"},{"task_slug":"policy-gradient-methods","task_name":"Policy Gradient Methods"}],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}