Decision Making with Side Information: A Causal Transport Robust Approach

Making Robust Contextual Decisions with Causal Transport Modern decision systems—from supply chains to financial planning—often rely on side information, such as customer attributes or environmental conditions, to guide better choices under uncertainty. Yet real-world data are imperfect, and naive models can fail when the underlying distribution changes. In the paper “Decision Making with Side Information: A Causal Transport Robust Approach,” the authors develop a new framework that integrates side information into distributionally robust optimization while preserving the causal structure between covariates and uncertain outcomes. The approach uses a causal transport distance to construct uncertainty sets that respect the conditional relationships learned from data. The authors show that the resulting worst-case distributions maintain this information structure and derive a tractable dual formulation for evaluating worst-case performance. For affine policies, the resulting optimization problem can be solved via convex programming, whereas more general settings reveal a new class of robust decision rules under convex costs.