Q-Learning under Finite Model Uncertainty
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910015774785536 |
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| author | Sester, Julian Decker, Cécile |
| author_facet | Sester, Julian Decker, Cécile |
| contents | We propose a robust Q-learning algorithm for Markov decision processes under model uncertainty when each state-action pair is associated with a finite ambiguity set of candidate transition kernels. This finite-measure framework enables highly flexible, user-designed uncertainty models and goes beyond the common KL and Wasserstein ball formulations. We establish almost sure convergence of the learned Q-function to the robust optimum, and derive non-asymptotic high-probability error bounds that separate stochastic approximation error from transition-kernel estimation error. Finally, we show that Wasserstein ball and parametric ambiguity sets can be approximated by finite ambiguity sets, allowing our algorithm to be used as a generic solver beyond the finite setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04259 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Q-Learning under Finite Model Uncertainty Sester, Julian Decker, Cécile Optimization and Control Artificial Intelligence Machine Learning Probability We propose a robust Q-learning algorithm for Markov decision processes under model uncertainty when each state-action pair is associated with a finite ambiguity set of candidate transition kernels. This finite-measure framework enables highly flexible, user-designed uncertainty models and goes beyond the common KL and Wasserstein ball formulations. We establish almost sure convergence of the learned Q-function to the robust optimum, and derive non-asymptotic high-probability error bounds that separate stochastic approximation error from transition-kernel estimation error. Finally, we show that Wasserstein ball and parametric ambiguity sets can be approximated by finite ambiguity sets, allowing our algorithm to be used as a generic solver beyond the finite setting. |
| title | Q-Learning under Finite Model Uncertainty |
| topic | Optimization and Control Artificial Intelligence Machine Learning Probability |
| url | https://arxiv.org/abs/2407.04259 |