# Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization

arXiv: https://arxiv.org/abs/1809.05504 · HTML: https://mlsanity.com/paper/1809.05504/

## Key facts

- Cited by 227 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2018.

## Built on by (most cited first, 30 of 227)

- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [Learning Iterative Reasoning through Energy Diffusion](https://mlsanity.com/paper/2406.11179/) (2024)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Learning Iterative Reasoning through Energy Minimization](https://mlsanity.com/paper/2206.15448/) (2022)
- [Backpropagation through Combinatorial Algorithms: Identity with Projection Works](https://mlsanity.com/paper/2205.15213/) (2022)
- [Learning with Combinatorial Optimization Layers: a Probabilistic Approach](https://mlsanity.com/paper/2207.13513/) (2022)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Learning Hard Optimization Problems: A Data Generation Perspective](https://mlsanity.com/paper/2106.02601/) (2021)
- [SurCo: Learning Linear Surrogates For Combinatorial Nonlinear Optimization Problems](https://mlsanity.com/paper/2210.12547/) (2022)
- [Direct Heterogeneous Causal Learning for Resource Allocation Problems in Marketing](https://mlsanity.com/paper/2211.15728/) (2022)
- [Fast Approximations for Job Shop Scheduling: A Lagrangian Dual Deep Learning Method](https://mlsanity.com/paper/2110.06365/) (2021)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [End-to-End Stochastic Optimization with Energy-Based Model](https://mlsanity.com/paper/2211.13837/) (2022)
- [Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimize](https://mlsanity.com/paper/2305.16830/) (2023)
- [Landscape Surrogate: Learning Decision Losses for Mathematical Optimization Under Partial Information](https://mlsanity.com/paper/2307.08964/) (2023)
- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Decision-Focused Learning with Directional Gradients](https://mlsanity.com/paper/2402.03256/) (2024)
- [Mechanistic Neural Networks for Scientific Machine Learning](https://mlsanity.com/paper/2402.13077/) (2024)
- [Learning Constrained Optimization with Deep Augmented Lagrangian Methods](https://mlsanity.com/paper/2403.03454/) (2024)
- [The Perils of Learning Before Optimizing](https://mlsanity.com/paper/2106.10349/) (2021)
- [End-to-End Conformal Calibration for Optimization Under Uncertainty](https://mlsanity.com/paper/2409.20534/) (2024)
- [Learning Revenue-Maximizing Auctions With Differentiable Matching](https://mlsanity.com/paper/2106.07877/) (2021)
- [Decision-Aware Learning for Optimizing Health Supply Chains](https://mlsanity.com/paper/2211.08507/) (2022)
- [Maximum Optimality Margin: A Unified Approach for Contextual Linear Programming and Inverse Linear Programming](https://mlsanity.com/paper/2301.11260/) (2023)
- [Backpropagation of Unrolled Solvers with Folded Optimization](https://mlsanity.com/paper/2301.12047/) (2023)

## Abstract (arXiv)

Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is first trained via a measure of predictive accuracy, and then its predictions are used as input into an optimization algorithm which produces a decision. However, the loss function used to train the model may easily be misaligned with the end goal, which is to make the best decisions possible. Hand-tuning the loss function to align with optimization is a difficult and error-prone process (which is often skipped entirely). We focus on combinatorial optimization problems and introduce a general framework for decision-focused learning, where the machine learning model is directly trained in conjunction with the optimization algorithm to produce high-quality decisions. Technically, our contribution is a means of integrating common classes of discrete optimization problems into deep learning or other predictive models, which are typically trained via gradient descent. The main idea is to use a continuous relaxation of the discrete problem to propagate gradients through the optimization procedure. We instantiate this framework for two broad classes of combinatorial problems: linear programs and submodular maximization. Experimental results across a variety of domains show that decision-focused learning often leads to improved optimization performance compared to traditional methods. We find that standard measures of accuracy are not a reliable proxy for a predictive model's utility in optimization, and our method's ability to specify the true goal as the model's training objective yields substantial dividends across a range of decision problems.