# Solver-Free Decision-Focused Learning for Linear Optimization Problems

arXiv: https://arxiv.org/abs/2505.22224 · HTML: https://mlsanity.com/paper/2505.22224/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 17 of 17)

- [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)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Learning with Fenchel-Young Losses](https://mlsanity.com/paper/1901.02324/) (2019)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [POPCORN: Partially Observed Prediction COnstrained ReiNforcement Learning](https://mlsanity.com/paper/2001.04032/) (2020)
- [Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimize](https://mlsanity.com/paper/2305.16830/) (2023)
- [Decision-Focused Learning without Differentiable Optimization: Learning Locally Optimized Decision Losses](https://mlsanity.com/paper/2203.16067/) (2022)
- [CaVE: A Cone-Aligned Approach for Fast Predict-then-optimize with Binary Linear Programs](https://mlsanity.com/paper/2312.07718/) (2023)
- [On Learning Prediction-Focused Mixtures](https://mlsanity.com/paper/2110.13221/) (2021)

## Built on by (most cited first, 9 of 9)

- [Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints](https://mlsanity.com/paper/2510.04951/) (2025)
- [Decision-Focused Learning via Tangent-Space Projection of Prediction Error](https://mlsanity.com/paper/2605.01361/) (2026)
- [A Solver-Free Training Method for Predict-then-Optimize](https://mlsanity.com/paper/2606.19587/) (2026)
- [Decision-Focused Learning: When and Why Traditional Prediction Models Fail](https://mlsanity.com/paper/2606.21773/) (2026)
- [DePICT: Decision-Preserving Interface for Constrained Downstream Tasks](https://mlsanity.com/paper/2610.03945/) (2026)
- [Scalable Decision-Focused Learning through Cost-Sensitive Regression](https://mlsanity.com/paper/2605.18005/) (2026)
- [Scaling Decision-Focused Learning to Large Problems with Lagrangian Decomposition](https://mlsanity.com/paper/2606.08797/) (2026)
- [Trustworthy synthetic data for campaign decision support: strategy simulation fidelity and the PolicySynth framework](https://mlsanity.com/paper/2607.11269/) (2026)
- [Decision-Driven Regularization: A Blended Model for Learning and Optimization](https://mlsanity.com/paper/2608.15124/) (2026)

## Abstract (arXiv)

Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from contextual features. This gives rise to predict-then-optimize problems, where a machine learning model predicts problem parameters that are then used to make decisions via optimization. A growing body of work on decision-focused learning (DFL) addresses this setting by training models specifically to produce predictions that maximize downstream decision quality, rather than accuracy. While effective, DFL is computationally expensive, because it requires solving the optimization problem with the predicted parameters at each loss evaluation. In this work, we address this computational bottleneck for linear optimization problems, a common class of problems in both DFL literature and real-world applications. We propose a solver-free training method that exploits the geometric structure of linear optimization to enable efficient training with minimal degradation in solution quality. Our method is based on the insight that a solution is optimal if and only if it achieves an objective value that is at least as good as that of its adjacent vertices on the feasible polytope. Building on this, our method compares the estimated quality of the ground-truth optimal solution with that of its precomputed adjacent vertices, and uses this as loss function. Experiments demonstrate that our method significantly reduces computational cost while maintaining high decision quality.