Distributionally Robust Optimisation with Bayesian Ambiguity Sets
This addresses decision-making under uncertainty for Bayesian models, but it is incremental as it builds on existing Bayesian DRO methodology.
The paper tackles the problem of sub-optimal decisions in Bayesian inference due to model uncertainty by introducing DRO-BAS, which optimizes worst-case risk over a posterior-informed ambiguity set, showing improved out-of-sample robustness in the Newsvendor problem.
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.