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

arXiv: https://arxiv.org/abs/2003.00360 · HTML: https://mlsanity.com/paper/2003.00360/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Feb 2020.

## Built on by (most cited first, 30 of 53)

- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Causal Decision Making and Causal Effect Estimation Are Not the Same... and Why It Matters](https://mlsanity.com/paper/2104.04103/) (2021)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Efficient differentiable quadratic programming layers: an ADMM approach](https://mlsanity.com/paper/2112.07464/) (2021)
- [Distributionally Robust End-to-End Portfolio Construction](https://mlsanity.com/paper/2206.05134/) (2022)
- [Learning Optimal Fair Classification Trees: Trade-offs Between Interpretability, Fairness, and Accuracy](https://mlsanity.com/paper/2201.09932/) (2022)
- [Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming](https://mlsanity.com/paper/2301.11260/) (2023)
- [Scalable Decision-Focused Learning in Restless Multi-Armed Bandits with Application to Maternal and Child Health](https://mlsanity.com/paper/2202.00916/) (2022)
- [Predict+Optimize for Packing and Covering LPs with Unknown Parameters in Constraints](https://mlsanity.com/paper/2209.03668/) (2022)
- [Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning](https://mlsanity.com/paper/2307.05213/) (2023)
- [Learning Optimal Prescriptive Trees from Observational Data](https://mlsanity.com/paper/2108.13628/) (2021)
- [Dissecting the Impact of Model Misspecification in Data-driven Optimization](https://mlsanity.com/paper/2503.00626/) (2025)
- [Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regime](https://mlsanity.com/paper/2311.07633/) (2023)
- [CaVE: A Cone-Aligned Approach for Fast Predict-then-optimize with Binary Linear Programs](https://mlsanity.com/paper/2312.07718/) (2023)
- [Allocation Requires Prediction Only if Inequality Is Low](https://mlsanity.com/paper/2406.13882/) (2024)
- [Explainable Data-Driven Optimization: From Context to Decision and Back Again](https://mlsanity.com/paper/2301.10074/) (2023)
- [Branch & Learn for Recursively and Iteratively Solvable Problems in Predict+Optimize](https://mlsanity.com/paper/2205.01672/) (2022)
- [Decision-Focused Evaluation of Worst-Case Distribution Shift](https://mlsanity.com/paper/2407.03557/) (2024)
- [PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planning](https://mlsanity.com/paper/2504.07383/) (2025)
- [Predict+Optimize Problem in Renewable Energy Scheduling](https://mlsanity.com/paper/2212.10723/) (2022)
- [WardropNet: Traffic Flow Predictions via Equilibrium-Augmented Learning](https://mlsanity.com/paper/2410.06656/) (2024)
- [Efficient End-to-End Learning for Decision-Making: A Meta-Optimization Approach](https://mlsanity.com/paper/2505.11360/) (2025)
- [Conformalized Decision Risk Assessment](https://mlsanity.com/paper/2505.13243/) (2025)
- [Prescriptive Machine Learning for Automated Decision Making: Challenges and Opportunities](https://mlsanity.com/paper/2112.08268/) (2021)
- [Learning Optimal Classification Trees Robust to Distribution Shifts](https://mlsanity.com/paper/2310.17772/) (2023)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)

## Abstract (arXiv)

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.