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.

翻译：本文研究参数不确定性下的扩散控制问题。基于插值估计的控制器可能因潜在的分布偏移而变得脆弱。通过在参数上引入先验的贝叶斯控制为这类偏移提供了基于信念的建模框架。然而，与任何贝叶斯模型类似，先验分布可能存在设定误差。为缓解设定误差并降低相较于经典鲁棒控制方法（例如\citet{hansen2008robustness}）的过度保守性，我们提出一种分布鲁棒贝叶斯控制（DRBC）框架，其中对手在基线先验的散度邻域内扰动先验分布。我们建立了强对偶性理论，将分布鲁棒先验评估简化为低维优化问题，并推导出适用于结构化策略参数化的实用仿真策略评估与学习算法。在线性二次控制仿真案例与真实数据投资组合选择问题中验证了算法的有效性。