Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control

Jose Blanchet, Jiayi Cheng, Yuewei Ling, Hao Liu and Yang Liu

Papers from arXiv.org

Abstract: 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.

Date: 2025-06, Revised 2026-01
New Economics Papers: this item is included in nep-cmp and nep-upt
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