Distributionally Robust Optimisation with Bayesian Ambiguity Sets

TL;DR

This paper introduces DRO-BAS, a distributionally robust optimization method that uses Bayesian ambiguity sets to improve decision-making under model uncertainty, demonstrating enhanced out-of-sample robustness in the Newsvendor problem.

Contribution

We propose a novel Bayesian ambiguity set-based DRO framework with a closed-form dual, improving robustness over existing Bayesian DRO methods.

Findings

Closed-form dual representation for exponential family models

Enhanced out-of-sample robustness in Newsvendor problem

Addresses model uncertainty with Bayesian-informed ambiguity sets

Abstract

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.