Smart "Predict, then Optimize"

TL;DR

The paper introduces the SPO framework, a novel approach that directly incorporates optimization problem structure into prediction models, leading to improved decision-making in predict-then-optimize tasks.

Contribution

It proposes the SPO loss and SPO+ surrogate loss, enabling prediction models to be trained specifically for optimization performance, with proven statistical consistency.

Findings

SPO framework improves decision quality in shortest path and portfolio problems.

Linear models trained with SPO+ outperform random forests in certain scenarios.

The SPO+ loss is convex and handles complex optimization problems efficiently.

Abstract

Many real-world analytics problems involve two significant challenges: prediction and optimization. Due to the typically complex nature of each challenge, the standard paradigm is predict-then-optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predictions will be used in the downstream optimization problem. In contrast, we propose a new and very general framework, called Smart "Predict, then Optimize" (SPO), which directly leverages the optimization problem structure, i.e., its objective and constraints, for designing better prediction models. A key component of our framework is the SPO loss function which measures the decision error induced by a prediction. Training a prediction model with respect to the SPO loss is computationally challenging, and thus we derive, using duality theory, a convex surrogate loss function which we call the SPO+ loss. Most importantly, we prove that the SPO+ loss is statistically consistent with respect to the SPO loss under mild conditions. Our SPO+ loss function can tractably handle any polyhedral, convex, or even mixed-integer optimization problem with a linear objective. Numerical experiments on shortest path and portfolio optimization problems show that the SPO framework can lead to significant improvement under the predict-then-optimize paradigm, in particular when the prediction model being trained is misspecified. We find that linear models trained using SPO+ loss tend to dominate random forest algorithms, even when the ground truth is highly nonlinear.