{"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/solving-long-run-average-reward-robust-mdps","title":"Solving Long-run Average Reward Robust MDPs via Stochastic Games","arxiv_id":"2312.13912","date":"2023-12-21","proceeding":null,"authors":["Krishnendu Chatterjee","Ehsan Kafshdar Goharshady","Mehrdad Karrabi","Petr Novotný","Đorđe Žikelić"],"abstract":"Markov decision processes (MDPs) provide a standard framework for sequential decision making under uncertainty. However, MDPs do not take uncertainty in transition probabilities into account. Robust Markov decision processes (RMDPs) address this shortcoming of MDPs by assigning to each transition an uncertainty set rather than a single probability value. In this work, we consider polytopic RMDPs in which all uncertainty sets are polytopes and study the problem of solving long-run average reward polytopic RMDPs. We present a novel perspective on this problem and show that it can be reduced to solving long-run average reward turn-based stochastic games with finite state and action spaces. This reduction allows us to derive several important consequences that were hitherto not known to hold for polytopic RMDPs. First, we derive new computational complexity bounds for solving long-run average reward polytopic RMDPs, showing for the first time that the threshold decision problem for them is in $NP \\cap coNP$ and that they admit a randomized algorithm with sub-exponential expected runtime. Second, we present Robust Polytopic Policy Iteration (RPPI), a novel policy iteration algorithm for solving long-run average reward polytopic RMDPs. Our experimental evaluation shows that RPPI is much more efficient in solving long-run average reward polytopic RMDPs compared to state-of-the-art methods based on value iteration.","url_abs":"https://arxiv.org/abs/2312.13912v2","url_pdf":"https://arxiv.org/pdf/2312.13912v2.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":"solving-long-run-average-reward-robust-mdps","repo_url":"https://github.com/mehrdad76/rmdp-lra","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"decision-making","task_name":"Decision Making"},{"task_slug":"decision-making-under-uncertainty","task_name":"Decision Making Under Uncertainty"},{"task_slug":"sequential-decision-making","task_name":"Sequential Decision Making"}],"methods":[{"method_slug":"focus","method_name":"Focus"},{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2312.13912","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2312.13912"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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