Revisiting Value Iteration: Unified Analysis of Discounted and Average-Reward Cases
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910048890912768 |
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| author | Mustafin, Arsenii Sheng, Xinyi Baumann, Dominik |
| author_facet | Mustafin, Arsenii Sheng, Xinyi Baumann, Dominik |
| contents | While Value Iteration (VI) is one of the most fundamental algorithms in Reinforcement Learning, its theoretical convergence guarantees still exhibit a persistent mismatch with empirical behavior. In the discounted-reward case, classical theory guarantees geometric convergence with rate $γ$, while in the average-reward case recent work suggests that only sublinear convergence can be expected. In practice, however, VI is often observed to converge significantly faster. In this work, we show through a unified geometry-based analysis that, under an assumption of a unique and unichain optimal policy, (i) convergence is geometric in both the discounted- and average-reward settings and (ii) the convergence rate is faster than previous analyses suggest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23914 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting Value Iteration: Unified Analysis of Discounted and Average-Reward Cases Mustafin, Arsenii Sheng, Xinyi Baumann, Dominik Machine Learning While Value Iteration (VI) is one of the most fundamental algorithms in Reinforcement Learning, its theoretical convergence guarantees still exhibit a persistent mismatch with empirical behavior. In the discounted-reward case, classical theory guarantees geometric convergence with rate $γ$, while in the average-reward case recent work suggests that only sublinear convergence can be expected. In practice, however, VI is often observed to converge significantly faster. In this work, we show through a unified geometry-based analysis that, under an assumption of a unique and unichain optimal policy, (i) convergence is geometric in both the discounted- and average-reward settings and (ii) the convergence rate is faster than previous analyses suggest. |
| title | Revisiting Value Iteration: Unified Analysis of Discounted and Average-Reward Cases |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.23914 |