Decision-Aware Predictions for Right-Hand Side Parameters in Linear Programs

TL;DR

This paper introduces a method for training prediction models to estimate LP parameters that ensure the predicted feasible region contains the true solution, improving decision accuracy.

Contribution

It proposes formulations that incorporate decision error and feasibility into training, with analysis and experiments demonstrating improved feasibility over standard regression.

Findings

Predicted feasible regions contain true solutions under certain conditions.

The proposed methods outperform standard regression in ensuring feasibility.

Numerical experiments validate the effectiveness of the approach.

Abstract

This paper studies an integrated learning and optimization problem in which a prediction model estimates the right-hand-side parameters of a linear program (LP) using a contextual vector. Considering that such a prediction alters the feasible region of the LP, we aim to estimate the constraint set to contain the optimal solution of the underlying LP, given by the true right-hand side parameters. We propose formulations for training a prediction model by minimizing the decision error while accounting for feasibility, measured by a collection of historical primal and dual solutions. Our analysis identifies conditions under which a resulting predicted feasible region contains the true solution, and whether the latter solution achieves optimality for the predicted problem. To solve the alternative training problems, we employ existing LP and nonconvex programming solution methods. We conduct numerical experiments on a synthetic LP and a network optimization problem. Our results indicate that the proposed methods effectively implement the desired feasibility, compared to standard regression models.