# Distributionally Robust Optimisation with Bayesian Ambiguity Sets

arXiv: https://arxiv.org/abs/2409.03492 · HTML: https://mlsanity.com/paper/2409.03492/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 5 Sep 2024.

## Builds on (most cited first, 7 of 7)

- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [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)

## Built on by (most cited first, 1 of 1)

- [Robust Predictive Uncertainty and Double Descent in Contaminated Bayesian Random Features](https://mlsanity.com/paper/2602.19126/) (2026)

## Abstract (arXiv)

Decision making under uncertainty is challenging since the data-generating process (DGP) is often unknown. Bayesian inference proceeds by estimating the DGP through posterior beliefs about the model's parameters. However, minimising the expected risk under these posterior beliefs can lead to sub-optimal 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 uncertainty in the model by optimising the worst-case risk over a posterior-informed ambiguity set. We show that our method admits a closed-form dual representation for many exponential family members and showcase its improved out-of-sample robustness against existing Bayesian DRO methodology in the Newsvendor problem.