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

Adam N. Elmachtoub, Jason Cheuk Nam Liang, Ryan Mcnellis
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:2858-2867, 2020.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-elmachtoub20a, title = {Decision Trees for Decision-Making under the Predict-then-Optimize Framework}, author = {Elmachtoub, Adam N. and Liang, Jason Cheuk Nam and Mcnellis, Ryan}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {2858--2867}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/elmachtoub20a/elmachtoub20a.pdf}, url = {https://proceedings.mlr.press/v119/elmachtoub20a.html}, 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.} }
Endnote
%0 Conference Paper %T Decision Trees for Decision-Making under the Predict-then-Optimize Framework %A Adam N. Elmachtoub %A Jason Cheuk Nam Liang %A Ryan Mcnellis %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-elmachtoub20a %I PMLR %P 2858--2867 %U https://proceedings.mlr.press/v119/elmachtoub20a.html %V 119 %X 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.
APA
Elmachtoub, A.N., Liang, J.C.N. & Mcnellis, R.. (2020). Decision Trees for Decision-Making under the Predict-then-Optimize Framework. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:2858-2867 Available from https://proceedings.mlr.press/v119/elmachtoub20a.html.

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