The voice of optimization
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10994_2020_5893_ReferencePDF.pdf
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322.33 KB
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014ea66cceec45e3a758e030a5b8a0e5
Author(s)
Bertsimas, Dimitris
Stellato, Bartolomeo
Date Issued
July 19, 2020
Publisher
Springer US
Version
Author's final manuscript
Abstract
Abstract
We introduce the idea that using optimal classification trees (OCTs) and optimal classification trees with-hyperplanes (OCT-Hs), interpretable machine learning algorithms developed by Bertsimas and Dunn (Mach Learn 106(7):1039–1082, 2017), we are able to obtain insight on the strategy behind the optimal solution in continuous and mixed-integer convex optimization problem as a function of key parameters that affect the problem. In this way, optimization is not a black box anymore. Instead, we redefine optimization as a multiclass classification problem where the predictor gives insights on the logic behind the optimal solution. In other words, OCTs and OCT-Hs give optimization a voice. We show on several realistic examples that the accuracy behind our method is in the 90–100% range, while even when the predictions are not correct, the degree of suboptimality or infeasibility is very low. We compare optimal strategy predictions of OCTs and OCT-Hs and feedforward neural networks (NNs) and conclude that the performance of OCT-Hs and NNs is comparable. OCTs are somewhat weaker but often competitive. Therefore, our approach provides a novel insightful understanding of optimal strategies to solve a broad class of continuous and mixed-integer optimization problems.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10994-020-05893-5
