Harita Dellaporta

Model-based Distributionally Robust Optimisation: Bayesian Ambiguity Sets and Model Misspecification

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 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. This talk will address this problem by introducing 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.  Simulations show DRO-BAS Pareto dominates existing Bayesian DRO formulations when evaluating the out-of-sample mean-variance trade-off, while achieving faster solve times. However, when the model is misspecified, this can lead to over-conservative decisions as the DGP might not be contained anymore in the ambiguity set. We will briefly discuss how Bayesian Ambiguity Sets can be easily adjusted to address this challenge by introducing DRO with Robust, to model misspecification, Bayesian Ambiguity Sets. These are expected Maximum Mean Discrepancy ambiguity sets under a robust posterior that incorporates beliefs about the DGP. The resulting optimisation problem obtains a dual formulation in the Reproducing Kernel Hilbert Space for any choice of model family.