Decision Trees for Decision-Making under the Predict-then-Optimize Framework

TL;DR

This paper introduces SPO Trees (SPOTs), a decision tree method optimized for decision-making tasks under the predict-then-optimize framework, focusing on minimizing decision suboptimality rather than prediction error.

Contribution

The paper proposes a novel decision tree training methodology called SPOTs that directly optimizes the SPO loss, enhancing decision quality and interpretability.

Findings

SPOTs outperform CART in decision quality on synthetic and real datasets.

SPOTs produce simpler models with lower complexity.

SPOTs achieve higher decision accuracy in travel time prediction and click probability estimation.

Abstract

We consider the use of decision trees for decision-making problems under the predict-then-optimize framework. That is, we would like to first use a decision tree to predict unknown input parameters of an optimization problem, and then make decisions by solving the optimization problem using the predicted parameters. A natural loss function in this framework is to measure the suboptimality of the decisions induced by the predicted input parameters, as opposed to measuring loss using input parameter prediction error. This natural loss function is known in the literature as the Smart Predict-then-Optimize (SPO) loss, and we propose a tractable methodology called SPO Trees (SPOTs) for training decision trees under this loss. SPOTs benefit from the interpretability of decision trees, providing an interpretable segmentation of contextual features into groups with distinct optimal solutions to the optimization problem of interest. We conduct several numerical experiments on synthetic and real data including the prediction of travel times for shortest path problems and predicting click probabilities for news article recommendation. We demonstrate on these datasets that SPOTs simultaneously provide higher quality decisions and significantly lower model complexity than other machine learning approaches (e.g., CART) trained to minimize prediction error.