# Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control

arXiv: https://arxiv.org/abs/2506.19294 · HTML: https://mlsanity.com/paper/2506.19294/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 57 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Builds on (most cited first, 26 of 26)

- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [Large-Scale Methods for Distributionally Robust Optimization](https://mlsanity.com/paper/2010.05893/) (2020)
- [An Optimal Algorithm for Bandit and Zero-Order Convex Optimization with Two-Point Feedback](https://mlsanity.com/paper/1507.08752/) (2015)
- [Recent Advances in Reinforcement Learning in Finance](https://mlsanity.com/paper/2112.04553/) (2021)
- [Understanding Warmup-Stable-Decay Learning Rates: A River Valley Loss Landscape Perspective](https://mlsanity.com/paper/2410.05192/) (2024)
- [Policy Gradient Method For Robust Reinforcement Learning](https://mlsanity.com/paper/2205.07344/) (2022)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [A Finite Sample Complexity Bound for Distributionally Robust Q-learning](https://mlsanity.com/paper/2302.13203/) (2023)
- [Statistical Analysis of Wasserstein Distributionally Robust Estimators](https://mlsanity.com/paper/2108.02120/) (2021)
- [Distributionally Robust Counterfactual Risk Minimization](https://mlsanity.com/paper/1906.06211/) (2019)
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- [Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances](https://mlsanity.com/paper/1802.04885/) (2018)
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- [Efficient Online Portfolio with Logarithmic Regret](https://mlsanity.com/paper/1805.07430/) (2018)
- [Distributionally Robust Batch Contextual Bandits](https://mlsanity.com/paper/2006.05630/) (2020)
- [Unbiased Multilevel Monte Carlo: Stochastic Optimization, Steady-state Simulation, Quantiles, and Other Applications](https://mlsanity.com/paper/1904.09929/) (2019)
- [On the Foundation of Distributionally Robust Reinforcement Learning](https://mlsanity.com/paper/2311.09018/) (2023)
- [Bayesian Distributionally Robust Optimization](https://mlsanity.com/paper/2112.08625/) (2021)
- [Semi-supervised Learning based on Distributionally Robust Optimization](https://mlsanity.com/paper/1702.08848/) (2017)
- [Data-Dependent Bounds for Online Portfolio Selection Without Lipschitzness and Smoothness](https://mlsanity.com/paper/2305.13946/) (2023)
- [A Globally Optimal Portfolio for m-Sparse Sharpe Ratio Maximization](https://mlsanity.com/paper/2410.21100/) (2024)
- [Optimal randomized multilevel Monte Carlo for repeatedly nested expectations](https://mlsanity.com/paper/2301.04095/) (2023)
- [Duality Theory for Robust Utility Maximisation](https://mlsanity.com/paper/2007.08376/) (2020)

## Abstract (arXiv)

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. citethansen2008robustness), 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.