# Automatically Learning Compact Quality-aware Surrogates for Optimization Problems

arXiv: https://arxiv.org/abs/2006.10815 · HTML: https://mlsanity.com/paper/2006.10815/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jun 2020.

## Built on by (most cited first, 22 of 22)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [SurCo: Learning Linear Surrogates For Combinatorial Nonlinear Optimization Problems](https://mlsanity.com/paper/2210.12547/) (2022)
- [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)
- [Decision-Aware Learning for Optimizing Health Supply Chains](https://mlsanity.com/paper/2211.08507/) (2022)
- [Decision-Focused Learning without Differentiable Optimization: Learning Locally Optimized Decision Losses](https://mlsanity.com/paper/2203.16067/) (2022)
- [Generalization Bound and Learning Methods for Data-Driven Projections in Linear Programming](https://mlsanity.com/paper/2309.00203/) (2023)
- [BPQP: A Differentiable Convex Optimization Framework for Efficient End-to-End Learning](https://mlsanity.com/paper/2411.19285/) (2024)
- [Benchmarking PtO and PnO Methods in the Predictive Combinatorial Optimization Regime](https://mlsanity.com/paper/2311.07633/) (2023)
- [Learning MDPs from Features: Predict-Then-Optimize for Sequential Decision Problems by Reinforcement Learning](https://mlsanity.com/paper/2106.03279/) (2021)
- [You Shall Pass: Dealing with the Zero-Gradient Problem in Predict and Optimize for Convex Optimization](https://mlsanity.com/paper/2307.16304/) (2023)
- [DF2: Distribution-Free Decision-Focused Learning](https://mlsanity.com/paper/2308.05889/) (2023)
- [A Solver-Free Training Method for Predict-then-Optimize](https://mlsanity.com/paper/2606.19587/) (2026)
- [A Surrogate Objective Framework for Prediction+Optimization with Soft Constraints](https://mlsanity.com/paper/2111.11358/) (2021)
- [Decision-focused Graph Neural Networks for Combinatorial Optimization](https://mlsanity.com/paper/2406.03647/) (2024)
- [What is the Right Notion of Distance between Predict-then-Optimize Tasks?](https://mlsanity.com/paper/2409.06997/) (2024)
- [Sufficient Decision Proxies for Decision-Focused Learning](https://mlsanity.com/paper/2505.03953/) (2025)
- [Beyond NaN: Resiliency of Optimization Layers in The Face of Infeasibility](https://mlsanity.com/paper/2202.06242/) (2022)
- [Parametric Nonconvex Optimization via Convex Surrogates](https://mlsanity.com/paper/2604.05640/) (2026)
- [Decision-Focused Learning: When and Why Traditional Prediction Models Fail](https://mlsanity.com/paper/2606.21773/) (2026)
- [RL-PaO: Prediction as Action in Decision Making under Uncertainty](https://mlsanity.com/paper/2609.37065/) (2026)

## Abstract (arXiv)

Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the optimization problem as a layer in the model training pipeline results in predictions of the unobserved parameters that lead to higher decision quality. Unfortunately, this process comes at a large computational cost because the optimization problem must be solved and differentiated through in each training iteration; furthermore, it may also sometimes fail to improve solution quality due to non-smoothness issues that arise when training through a complex optimization layer. To address these shortcomings, we learn a low-dimensional surrogate model of a large optimization problem by representing the feasible space in terms of meta-variables, each of which is a linear combination of the original variables. By training a low-dimensional surrogate model end-to-end, and jointly with the predictive model, we achieve: i) a large reduction in training and inference time; and ii) improved performance by focusing attention on the more important variables in the optimization and learning in a smoother space. Empirically, we demonstrate these improvements on a non-convex adversary modeling task, a submodular recommendation task and a convex portfolio optimization task.