Faster Fixed-Point Methods for Multichain MDPs
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Abstract (arXiv)
We study value-iteration (VI) algorithms for solving general (a.k.a. multichain) Markov decision processes (MDPs) under the average-reward criterion, a fundamental but theoretically challenging setting. Beyond the difficulties inherent to all average-reward problems posed by the lack of contractivity and non-uniqueness of solutions to the Bellman operator, in the multichain setting an optimal policy must solve the navigation subproblem of steering towards the best connected component, in addition to optimizing long-run performance within each component. We develop algorithms which better solve this navigational subproblem in order to achieve faster convergence for multichain MDPs, obtaining improved rates of convergence and sharper measures of complexity relative to prior work. Many key components of our results are of potential independent interest, including novel connections between average-reward and discounted problems, optimal fixed-point methods for discounted VI which extend to general Banach spaces, new sublinear convergence rates for the discounted value error, and refined suboptimality decompositions for multichain MDPs. Overall our results yield faster convergence rates for discounted and average-reward problems and expand the theoretical foundations of VI approaches.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 14 of its 33 references that are in the map. First posted on arXiv 26 Jun 2025.
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14 of 33 references.
References · 14
- 2017A First Order Method for Solving Convex Bi-Level Optimization Problemscited by 67
- 2018Efficient Bias-Span-Constrained Exploration-Exploitation in Reinforcement Learningcited by 66
- 2021Towards Tight Bounds on the Sample Complexity of Average-reward MDPscited by 33
- 2022Near Sample-Optimal Reduction-based Policy Learning for Average Reward MDPcited by 29
- 2022Exact Optimal Accelerated Complexity for Fixed-Point Iterationscited by 25
- 2019A First-Order Approach To Accelerated Value Iterationcited by 17
- 2024Span-Based Optimal Sample Complexity for Weakly Communicating and General Average Reward MDPscited by 17
- 2021Optimal error bounds for nonexpansive fixed-point iterations in normed spacescited by 12
- 2024Stochastic Halpern iteration in normed spaces and applications to reinforcement learningcited by 12
- 2023Accelerating Value Iteration with Anchoringcited by 11
- 2024The Plug-in Approach for Average-Reward and Discounted MDPs: Optimal Sample Complexity Analysiscited by 9
- 2025Optimal Non-Asymptotic Rates of Value Iteration for Average-Reward Markov Decision Processescited by 6
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Citing papers per year: 2026: 2.
2 papers.