# Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Sets

arXiv: https://arxiv.org/abs/2411.16829 · HTML: https://mlsanity.com/paper/2411.16829/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 13 of 13)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [Distributionally Robust Optimization and Generalization in Kernel Methods](https://mlsanity.com/paper/1905.10943/) (2019)
- [Modeling the Second Player in Distributionally Robust Optimization](https://mlsanity.com/paper/2103.10282/) (2021)
- [Optimal Bounds between f-Divergences and Integral Probability Metrics](https://mlsanity.com/paper/2006.05973/) (2020)
- [Distributionally Robust Models with Parametric Likelihood Ratios](https://mlsanity.com/paper/2204.06340/) (2022)
- [Bayesian Distributionally Robust Optimization](https://mlsanity.com/paper/2112.08625/) (2021)
- [Calibration of Distributionally Robust Empirical Optimization Models](https://mlsanity.com/paper/1711.06565/) (2017)
- [Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificity](https://mlsanity.com/paper/2301.13565/) (2023)

## Built on by (most cited first, 3 of 3)

- [Nested Expectations with Kernel Quadrature](https://mlsanity.com/paper/2502.18284/) (2025)
- [Decision Making under Model Misspecification: DRO with Robust Bayesian Ambiguity Sets](https://mlsanity.com/paper/2505.03585/) (2025)
- [Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination](https://mlsanity.com/paper/2601.21324/) (2026)

## Abstract (arXiv)

Decision making under uncertainty is challenging as the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs on the model's parameters. However, minimising the expected risk under these beliefs can lead to suboptimal decisions due to model uncertainty or limited, noisy observations. To address this, we introduce Distributionally Robust Optimisation with Bayesian Ambiguity Sets (DRO-BAS) which hedges against model uncertainty by optimising the worst-case risk over a posterior-informed ambiguity set. We provide two such sets, based on posterior expectations (DRO-BAS(PE)) or posterior predictives (DRO-BAS(PP)) and prove that both admit, under conditions, strong dual formulations leading to efficient single-stage stochastic programs which are solved with a sample average approximation. For DRO-BAS(PE) this covers all conjugate exponential family members while for DRO-BAS(PP) this is shown under conditions on the predictive's moment generating function. Our DRO-BAS formulations outperform existing Bayesian DRO on the Newsvendor problem and achieve faster solve times with comparable robustness on the Portfolio problem.