Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917235785728000 |
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| author | Blanchet, Jose Cheng, Jiayi Ling, Yuewei Liu, Hao Liu, Yang |
| author_facet | Blanchet, Jose Cheng, Jiayi Ling, Yuewei Liu, Hao Liu, Yang |
| contents | We study diffusion control problems under parameter uncertainty. Controllers based on plug-in estimation can be brittle due to potential distribution shifts. Bayesian control with a prior on the parameters offers a formulation with beliefs about such shifts. However, as with any Bayesian model, the prior may be misspecified. To mitigate misspecification and reduce over-pessimism compared to classical robust control approaches (e.g. \citet{hansen2008robustness}), we propose a distributionally robust Bayesian control (DRBC) formulation in which an adversary perturbs the prior within a divergence neighborhood of a baseline prior. We develop a strong duality result that reduces the distributionally robust prior evaluation to a low-dimensional optimization and yields a practical simulation-based policy evaluation and learning procedure with structured policy parameterizations. We validate the efficiency of the algorithm on a synthetic linear-quadratic control example and real-data portfolio selection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control Blanchet, Jose Cheng, Jiayi Ling, Yuewei Liu, Hao Liu, Yang Optimization and Control Probability Portfolio Management Machine Learning We study diffusion control problems under parameter uncertainty. Controllers based on plug-in estimation can be brittle due to potential distribution shifts. Bayesian control with a prior on the parameters offers a formulation with beliefs about such shifts. However, as with any Bayesian model, the prior may be misspecified. To mitigate misspecification and reduce over-pessimism compared to classical robust control approaches (e.g. \citet{hansen2008robustness}), we propose a distributionally robust Bayesian control (DRBC) formulation in which an adversary perturbs the prior within a divergence neighborhood of a baseline prior. We develop a strong duality result that reduces the distributionally robust prior evaluation to a low-dimensional optimization and yields a practical simulation-based policy evaluation and learning procedure with structured policy parameterizations. We validate the efficiency of the algorithm on a synthetic linear-quadratic control example and real-data portfolio selection. |
| title | Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control |
| topic | Optimization and Control Probability Portfolio Management Machine Learning |
| url | https://arxiv.org/abs/2506.19294 |