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.

中文翻译：

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优化之声

我们介绍了使用最佳分类树 (OCT) 和具有超平面的最佳分类树 (OCT-Hs) 的想法，Bertsimas 和 Dunn (Mach Learn 106(7):1039–1082, 2017) 开发的可解释机器学习算法，我们能够深入了解连续和混合整数凸优化问题中最优解背后的策略，作为影响问题的关键参数的函数。通过这种方式，优化不再是一个黑匣子。相反，我们将优化重新定义为一个多类分类问题，其中预测器可以洞察最佳解决方案背后的逻辑。换句话说，OCT 和 OCT-H 为优化提供了声音。我们在几个现实例子中展示了我们方法背后的准确率在 90-100% 范围内，而即使预测不正确，次优或不可行的程度非常低。我们比较了 OCTs 和 OCT-Hs 和前馈神经网络 (NNs) 的最佳策略预测，并得出结论，OCT-Hs 和 NNs 的性能是可比的。OCT 稍弱，但通常具有竞争力。因此，我们的方法提供了对解决一系列连续和混合整数优化问题的最佳策略的新见解。