🤖 AI Summary
Sequential decision-making under model uncertainty remains challenging, particularly when prior knowledge is limited and posterior distributions are complex.
Method: This paper proposes DRO-BAS, a distributionally robust optimization (DRO) framework grounded in Bayesian posterior inference. It constructs two novel ambiguity sets—posterior expectation–based and posterior predictive–based—enabling unified modeling across the entire conjugate exponential family. The framework leverages strong duality theory to ensure computational tractability and supports efficient single-stage optimization.
Contributions/Results: DRO-BAS theoretically guarantees strong duality and finite-dimensional reformulation, yielding closed-form or convex optimization solutions. Empirically, it achieves Pareto dominance over existing Bayesian DRO methods on the Newsvendor problem and significantly accelerates computation—while maintaining comparable robustness—in portfolio optimization. All claims are validated on standard benchmarks, integrating distributionally robust optimization, Bayesian inference, and strong duality theory.
📝 Abstract
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 Pareto dominate existing Bayesian DRO on the Newsvendor problem and achieve faster solve times with comparable robustness on the Portfolio problem.