Stochastic Optimal Control with Side Information and Bayesian Learning
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910033056366592 |
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| author | Milz, Johannes Shapiro, Alexander Zhou, Enlu |
| author_facet | Milz, Johannes Shapiro, Alexander Zhou, Enlu |
| contents | We study infinite-horizon stochastic optimal control problems with observable side information: a Markov chain that modulates an unknown context-conditional randomness distribution. Since this distribution is unknown, we propose a Bayesian reformulation based on a parametric density model and posterior predictive dynamics, which yields a Bayesian Bellman equation. We prove posterior consistency under Markov samples and, under correct specification and identifiability, uniform convergence of the Bayesian value function. Finally, we establish Bernstein--von Mises-type asymptotic normality for the data-driven contextual optimal value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22047 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Optimal Control with Side Information and Bayesian Learning Milz, Johannes Shapiro, Alexander Zhou, Enlu Optimization and Control Statistics Theory We study infinite-horizon stochastic optimal control problems with observable side information: a Markov chain that modulates an unknown context-conditional randomness distribution. Since this distribution is unknown, we propose a Bayesian reformulation based on a parametric density model and posterior predictive dynamics, which yields a Bayesian Bellman equation. We prove posterior consistency under Markov samples and, under correct specification and identifiability, uniform convergence of the Bayesian value function. Finally, we establish Bernstein--von Mises-type asymptotic normality for the data-driven contextual optimal value. |
| title | Stochastic Optimal Control with Side Information and Bayesian Learning |
| topic | Optimization and Control Statistics Theory |
| url | https://arxiv.org/abs/2602.22047 |