Optimal Non-Asymptotic Rates of Value Iteration for Average-Reward Markov Decision Processes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908821211840512 |
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| author | Lee, Jongmin Ryu, Ernest K. |
| author_facet | Lee, Jongmin Ryu, Ernest K. |
| contents | While there is an extensive body of research on the analysis of Value Iteration (VI) for discounted cumulative-reward MDPs, prior work on analyzing VI for (undiscounted) average-reward MDPs has been limited, and most prior results focus on asymptotic rates in terms of Bellman error. In this work, we conduct refined non-asymptotic analyses of average-reward MDPs, obtaining a collection of convergence results that advance our understanding of the setup. Among our new results, most notable are the $\mathcal{O}(1/k)$-rates of Anchored Value Iteration on the Bellman error under the multichain setup and the span-based complexity lower bound that matches the $\mathcal{O}(1/k)$ upper bound up to a constant factor of $8$ in the weakly communicating and unichain setups |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_09913 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Non-Asymptotic Rates of Value Iteration for Average-Reward Markov Decision Processes Lee, Jongmin Ryu, Ernest K. Optimization and Control While there is an extensive body of research on the analysis of Value Iteration (VI) for discounted cumulative-reward MDPs, prior work on analyzing VI for (undiscounted) average-reward MDPs has been limited, and most prior results focus on asymptotic rates in terms of Bellman error. In this work, we conduct refined non-asymptotic analyses of average-reward MDPs, obtaining a collection of convergence results that advance our understanding of the setup. Among our new results, most notable are the $\mathcal{O}(1/k)$-rates of Anchored Value Iteration on the Bellman error under the multichain setup and the span-based complexity lower bound that matches the $\mathcal{O}(1/k)$ upper bound up to a constant factor of $8$ in the weakly communicating and unichain setups |
| title | Optimal Non-Asymptotic Rates of Value Iteration for Average-Reward Markov Decision Processes |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.09913 |