Partially Observed Optimal Stochastic Control: Regularity, Optimality, Approximations, and Learning
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929653475704832 |
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| author | Kara, Ali Devran Yuksel, Serdar |
| author_facet | Kara, Ali Devran Yuksel, Serdar |
| contents | In this review/tutorial article, we present recent progress on optimal control of partially observed Markov Decision Processes (POMDPs). We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where these constitute weak Feller and Wasserstein regularity and controlled filter stability. These are then utilized to arrive at existence results on optimal policies for both discounted and average cost problems, and regularity of value functions. Then, we study rigorous approximation results involving quantization based finite model approximations as well as finite window approximations under controlled filter stability. Finally, we present several recent reinforcement learning theoretic results which rigorously establish convergence to near optimality under both criteria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partially Observed Optimal Stochastic Control: Regularity, Optimality, Approximations, and Learning Kara, Ali Devran Yuksel, Serdar Optimization and Control Systems and Control In this review/tutorial article, we present recent progress on optimal control of partially observed Markov Decision Processes (POMDPs). We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where these constitute weak Feller and Wasserstein regularity and controlled filter stability. These are then utilized to arrive at existence results on optimal policies for both discounted and average cost problems, and regularity of value functions. Then, we study rigorous approximation results involving quantization based finite model approximations as well as finite window approximations under controlled filter stability. Finally, we present several recent reinforcement learning theoretic results which rigorously establish convergence to near optimality under both criteria. |
| title | Partially Observed Optimal Stochastic Control: Regularity, Optimality, Approximations, and Learning |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2412.06735 |