# Bayesian Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2112.08625 · HTML: https://mlsanity.com/paper/2112.08625/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2021.

## Built on by (most cited first, 16 of 16)

- [Distributionally Robust Bayesian Optimization with varphi-divergences](https://mlsanity.com/paper/2203.02128/) (2022)
- [Robust Expected Information Gain for Optimal Bayesian Experimental Design Using Ambiguity Sets](https://mlsanity.com/paper/2205.09914/) (2022)
- [Nested Expectations with Kernel Quadrature](https://mlsanity.com/paper/2502.18284/) (2025)
- [DRO: A Python Library for Distributionally Robust Optimization in Machine Learning](https://mlsanity.com/paper/2505.23565/) (2025)
- [Federated Distributionally Robust Optimization with Non-Convex Objectives: Algorithm and Analysis](https://mlsanity.com/paper/2307.14364/) (2023)
- [On the convergence rate of noisy Bayesian Optimization with Expected Improvement](https://mlsanity.com/paper/2501.09262/) (2025)
- [Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Sets](https://mlsanity.com/paper/2411.16829/) (2024)
- [Nested Stochastic Algorithm for Generalized Sinkhorn distance-Regularized Distributionally Robust Optimization](https://mlsanity.com/paper/2503.22923/) (2025)
- [Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets](https://mlsanity.com/paper/2505.03585/) (2025)
- [Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization](https://mlsanity.com/paper/2401.15771/) (2024)
- [Distributionally Robust Optimisation with Bayesian Ambiguity Sets](https://mlsanity.com/paper/2409.03492/) (2024)
- [Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination](https://mlsanity.com/paper/2601.21324/) (2026)
- [Differentiability and Approximation of Probability Functions under Gaussian Mixture Models](https://mlsanity.com/paper/2411.02721/) (2024)
- [Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control](https://mlsanity.com/paper/2506.19294/) (2025)
- [Bayesian Risk-Sensitive Policy Optimization For MDPs With General Loss Functions](https://mlsanity.com/paper/2509.15509/) (2025)
- [Maximally Robust Satisficing Bayesian Optimization](https://mlsanity.com/paper/2607.13652/) (2026)

## Abstract (arXiv)

We introduce a new framework, Bayesian Distributionally Robust Optimization (Bayesian-DRO), for data-driven stochastic optimization where the underlying distribution is unknown. Bayesian-DRO contrasts with most of the existing DRO approaches in the use of Bayesian estimation of the unknown distribution. To make computation of Bayesian updating tractable, Bayesian-DRO first assumes the underlying distribution takes a parametric form with unknown parameter and then computes the posterior distribution of the parameter. To address the model uncertainty brought by the assumed parametric distribution, Bayesian-DRO constructs an ambiguity set of distributions with the assumed parametric distribution as the reference distribution and then optimizes with respect to the worst case in the ambiguity set. We show the consistency of the Bayesian posterior distribution and subsequently the convergence of objective functions and optimal solutions of Bayesian-DRO. Our consistency result of the Bayesian posterior requires simpler assumptions than the classical literature on Bayesian consistency. We also consider several approaches for selecting the ambiguity set size in Bayesian-DRO and compare them numerically. Our numerical experiments demonstrate the out-of-sample performance of Bayesian-DRO in comparison with Kullback-Leibler-based (KL-) and Wasserstein-based empirical DRO as well as risk-neutral Bayesian Risk Optimization. Our numerical results shed light on how to choose the modeling framework (Bayesian-DRO, KL-DRO, Wasserstein-DRO) for specific problems, but the choice for general problems still remains an important and open question.