Abstract: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.
From: Johannes Milz [view email]
[v1]
Wed, 25 Feb 2026 15:56:14 UTC (20 KB)
[v2]
Mon, 20 Jul 2026 19:58:57 UTC (28 KB)
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