# The Voice of Optimization

arXiv: https://arxiv.org/abs/1812.09991 · HTML: https://mlsanity.com/paper/1812.09991/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2018.

## Built on by (most cited first, 28 of 28)

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- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [Strong Optimal Classification Trees](https://mlsanity.com/paper/2103.15965/) (2021)
- [OptiChat: Bridging Optimization Models and Practitioners with Large Language Models](https://mlsanity.com/paper/2501.08406/) (2025)
- [Aligning Diffusion Model with Problem Constraints for Trajectory Optimization](https://mlsanity.com/paper/2504.00342/) (2025)
- [An actor-critic algorithm with policy gradients to solve the job shop scheduling problem using deep double recurrent agents](https://mlsanity.com/paper/2110.09076/) (2021)
- [Metric Learning to Accelerate Convergence of Operator Splitting Methods for Differentiable Parametric Programming](https://mlsanity.com/paper/2404.00882/) (2024)
- [Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initialize](https://mlsanity.com/paper/2310.07082/) (2023)
- [Improving Computational Efficiency for Powered Descent Guidance via Transformer-based Tight Constraint Prediction](https://mlsanity.com/paper/2311.05135/) (2023)
- [An Expandable Machine Learning-Optimization Framework to Sequential Decision-Making](https://mlsanity.com/paper/2311.06972/) (2023)
- [NeuralQP: A General Hypergraph-based Optimization Framework for Large-scale QCQPs](https://mlsanity.com/paper/2410.03720/) (2024)
- [Learning Multiple Initial Solutions to Optimization Problems](https://mlsanity.com/paper/2411.02158/) (2024)
- [A Machine Learning Approach to Two-Stage Adaptive Robust Optimization](https://mlsanity.com/paper/2307.12409/) (2023)
- [Differentiable Cutting-plane Layers for Mixed-integer Linear Optimization](https://mlsanity.com/paper/2311.03350/) (2023)
- [Generative deep learning for decision making in gas networks](https://mlsanity.com/paper/2102.02125/) (2021)
- [Lightweight Online Learning for Sets of Related Problems in Automated Reasoning](https://mlsanity.com/paper/2305.11087/) (2023)
- [Grid-SiPhyR: An end-to-end learning to optimize framework for combinatorial problems in power systems](https://mlsanity.com/paper/2206.06789/) (2022)
- [Optimal Control of Multiclass Fluid Queueing Networks: A Machine Learning Approach](https://mlsanity.com/paper/2307.12405/) (2023)
- [Automatic Construction of Clinical Scoring Systems with LLM Agents](https://mlsanity.com/paper/2601.22324/) (2026)
- [GLENS: Global Search via Learning from Solver Iterates with Diffusion Models](https://mlsanity.com/paper/2606.00366/) (2026)
- [(Machine) Learning to Improve the Empirical Performance of Discrete Algorithms](https://mlsanity.com/paper/2109.14271/) (2021)
- [A Sequential Deep Learning Algorithm for Sampled Mixed-integer Optimisation Problems](https://mlsanity.com/paper/2301.10703/) (2023)
- [Towards An Unsupervised Learning Scheme for Efficiently Solving Parameterized Mixed-Integer Programs](https://mlsanity.com/paper/2412.17623/) (2024)
- [EvoOpt-LLM: Evolving industrial optimization models with large language models](https://mlsanity.com/paper/2602.01082/) (2026)

## Abstract (arXiv)

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 [2017, 2018], 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.