Uncertainty Sets for Distributionally Robust Bandits Using Structural Equation Models

Abstract

Distributionally robust evaluation estimates the worst-case expected return over an uncertainty set of possible covariate and reward distributions, and distributionally robust learning finds a policy that maximizes that worst-case return across that uncertainty set. Unfortunately, current methods for distributionally robust evaluation and learning create overly conservative evaluations and policies. In this work, we propose a practical bandit evaluation and learning algorithm that tailors the uncertainty set to specific problems using mathematical programs constrained by structural equation models. Further, we show how conditional independence testing can be used to detect shifted variables for modeling. We find that the structural equation model (SEM) approach gives more accurate evaluations and learns lower-variance policies than traditional approaches, particularly for large shifts. Further, the SEM approach learns an optimal policy, assuming the model is sufficiently well-specified.