Bounding the Difference between the Values of Robust and Non-Robust Markov Decision Problems
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866918002733088768 |
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| author | Neufeld, Ariel Sester, Julian |
| author_facet | Neufeld, Ariel Sester, Julian |
| contents | In this note we provide an upper bound for the difference between the value function of a distributionally robust Markov decision problem and the value function of a non-robust Markov decision problem, where the ambiguity set of probability kernels of the distributionally robust Markov decision process is described by a Wasserstein-ball around some reference kernel whereas the non-robust Markov decision process behaves according to a fixed probability kernel contained in the ambiguity set. Our derived upper bound for the difference between the value functions is dimension-free and depends linearly on the radius of the Wasserstein-ball. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_05520 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounding the Difference between the Values of Robust and Non-Robust Markov Decision Problems Neufeld, Ariel Sester, Julian Optimization and Control Probability In this note we provide an upper bound for the difference between the value function of a distributionally robust Markov decision problem and the value function of a non-robust Markov decision problem, where the ambiguity set of probability kernels of the distributionally robust Markov decision process is described by a Wasserstein-ball around some reference kernel whereas the non-robust Markov decision process behaves according to a fixed probability kernel contained in the ambiguity set. Our derived upper bound for the difference between the value functions is dimension-free and depends linearly on the radius of the Wasserstein-ball. |
| title | Bounding the Difference between the Values of Robust and Non-Robust Markov Decision Problems |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2308.05520 |