Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints
This work addresses robust decision-making under uncertainty in optimization problems, which is incremental as it extends existing methods to handle constraint uncertainty more effectively.
The paper tackles the problem of contextual stochastic linear optimization with uncertain constraints predicted by machine learning models, introducing a feasibility-sensitive loss function and a convex surrogate that effectively handle constraint uncertainty, demonstrating improved performance on fractional knapsack and alloy production instances.
We study an extension of contextual stochastic linear optimization (CSLO) that, in contrast to most of the existing literature, involves inequality constraints that depend on uncertain parameters predicted by a machine learning model. To handle the constraint uncertainty, we use contextual uncertainty sets constructed via methods like conformal prediction. Given a contextual uncertainty set method, we introduce the "Smart Predict-then-Optimize with Robust Constraints" (SPO-RC) loss, a feasibility-sensitive adaptation of the SPO loss that measures decision error of predicted objective parameters. We also introduce a convex surrogate, SPO-RC+, and prove Fisher consistency with SPO-RC. To enhance performance, we train on truncated datasets where true constraint parameters lie within the uncertainty sets, and we correct the induced sample selection bias using importance reweighting techniques. Through experiments on fractional knapsack and alloy production problem instances, we demonstrate that SPO-RC+ effectively handles uncertainty in constraints and that combining truncation with importance reweighting can further improve performance.