# The Perils of Learning Before Optimizing

arXiv: https://arxiv.org/abs/2106.10349 · HTML: https://mlsanity.com/paper/2106.10349/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 18 Jun 2021.

## Builds on (most cited first, 9 of 9)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [End to end learning and optimization on graphs](https://mlsanity.com/paper/1905.13732/) (2019)
- [On the Differentiability of the Solution to Convex Optimization Problems](https://mlsanity.com/paper/1804.05098/) (2018)
- [Differentiable Submodular Maximization](https://mlsanity.com/paper/1803.01785/) (2018)

## Built on by (most cited first, 15 of 15)

- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Decision-Focused Learning without Differentiable Optimization: Learning Locally Optimized Decision Losses](https://mlsanity.com/paper/2203.16067/) (2022)
- [Artificial Intelligence for Operations Research: Revolutionizing the Operations Research Process](https://mlsanity.com/paper/2401.03244/) (2024)
- [Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regime](https://mlsanity.com/paper/2311.07633/) (2023)
- [From Inverse Optimization to Feasibility to ERM](https://mlsanity.com/paper/2402.17890/) (2024)
- [Efficient End-to-End Learning for Decision-Making: A Meta-Optimization Approach](https://mlsanity.com/paper/2505.11360/) (2025)
- [Improving Feasibility via Fast Autoencoder-Based Projections](https://mlsanity.com/paper/2604.03489/) (2026)
- [How to predict and optimise with asymmetric error metrics](https://mlsanity.com/paper/2211.13586/) (2022)
- [Sufficient Decision Proxies for Decision-Focused Learning](https://mlsanity.com/paper/2505.03953/) (2025)
- [Accuracy Is Not Service: A Decision-Aware Benchmark for Intermittent-Demand Forecasting](https://mlsanity.com/paper/2609.13840/) (2026)
- [On the Robustness of Decision-Focused Learning](https://mlsanity.com/paper/2311.16487/) (2023)
- [OPO: Making Decision-Focused Data Acquisition Decisions](https://mlsanity.com/paper/2504.15062/) (2025)
- [Simulating Classification Models for Ex-Ante Evaluation of Predict-Then-Optimize Methods](https://mlsanity.com/paper/2509.02191/) (2025)
- [Managing Solution Stability in Decision-Focused Learning with Cost Regularization](https://mlsanity.com/paper/2601.21883/) (2026)
- [When May a Model Replace the Experiment? Audits, Licenses, and the Price of Trust in Surrogate-Driven Design](https://mlsanity.com/paper/2608.01378/) (2026)

## Abstract (arXiv)

Formulating real-world optimization problems often begins with making predictions from historical data (e.g., an optimizer that aims to recommend fast routes relies upon travel-time predictions). Typically, learning the prediction model used to generate the optimization problem and solving that problem are performed in two separate stages. Recent work has showed how such prediction models can be learned end-to-end by differentiating through the optimization task. Such methods often yield empirical improvements, which are typically attributed to end-to-end making better error tradeoffs than the standard loss function used in a two-stage solution. We refine this explanation and more precisely characterize when end-to-end can improve performance. When prediction targets are stochastic, a two-stage solution must make an a priori choice about which statistics of the target distribution to model-we consider expectations over prediction targets-while an end-to-end solution can make this choice adaptively. We show that the performance gap between a two-stage and end-to-end approach is closely related to the price of correlation concept in stochastic optimization and show the implications of some existing POC results for the predict-then-optimize problem. We then consider a novel and particularly practical setting, where multiple prediction targets are combined to obtain each of the objective function's coefficients. We give explicit constructions where (1) two-stage performs unboundedly worse than end-to-end; and (2) two-stage is optimal. We use simulations to experimentally quantify performance gaps and identify a wide range of real-world applications from the literature whose objective functions rely on multiple prediction targets, suggesting that end-to-end learning could yield significant improvements.