Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints

TL;DR

This paper introduces a new loss function and surrogate for robust stochastic linear optimization with uncertain constraints, improving decision accuracy by handling constraint uncertainty effectively.

Contribution

It proposes the SPO-RC loss and SPO-RC+ surrogate, incorporating uncertainty sets and bias correction techniques for better optimization under uncertainty.

Findings

SPO-RC+ effectively manages constraint uncertainty in experiments.

Truncated datasets combined with importance reweighting improve performance.

The methods outperform existing approaches in knapsack and alloy production tasks.

Abstract

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.