# Contrastive Losses and Solution Caching for Predict-and-Optimize

arXiv: https://arxiv.org/abs/2011.05354 · HTML: https://mlsanity.com/paper/2011.05354/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2020.

## Built on by (most cited first, 30 of 52)

- [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)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2302.01578/) (2023)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Learning with Combinatorial Optimization Layers: a Probabilistic Approach](https://mlsanity.com/paper/2207.13513/) (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)
- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Controlling Continuous Relaxation for Combinatorial Optimization](https://mlsanity.com/paper/2309.16965/) (2023)
- [Decision-Focused Learning without Differentiable Optimization: Learning Locally Optimized Decision Losses](https://mlsanity.com/paper/2203.16067/) (2022)
- [Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning](https://mlsanity.com/paper/2307.05213/) (2023)
- [Decision Focused Causal Learning for Direct Counterfactual Marketing Optimization](https://mlsanity.com/paper/2407.13664/) (2024)
- [Solver-Free Decision-Focused Learning for Linear Optimization Problems](https://mlsanity.com/paper/2505.22224/) (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)
- [Differentiable Distributionally Robust Optimization Layers](https://mlsanity.com/paper/2406.16571/) (2024)
- [ROI-Reasoning: Rational Optimization for Inference via Pre-Computation Meta-Cognition](https://mlsanity.com/paper/2601.03822/) (2026)
- [Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints](https://mlsanity.com/paper/2510.04951/) (2025)
- [Robust Losses for Decision-Focused Learning](https://mlsanity.com/paper/2310.04328/) (2023)
- [Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2401.10467/) (2024)
- [Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models](https://mlsanity.com/paper/2409.09684/) (2024)
- [Decision-Focused Evaluation of Worst-Case Distribution Shift](https://mlsanity.com/paper/2407.03557/) (2024)
- [Decision-Focused Learning via Tangent-Space Projection of Prediction Error](https://mlsanity.com/paper/2605.01361/) (2026)
- [Continuous Parallel Relaxation for Finding Diverse Solutions in Combinatorial Optimization Problems](https://mlsanity.com/paper/2402.02190/) (2024)
- [Locally Convex Global Loss Network for Decision-Focused Learning](https://mlsanity.com/paper/2403.01875/) (2024)
- [Generalized Decision Focused Learning under Imprecise Uncertainty--Theoretical Study](https://mlsanity.com/paper/2502.17984/) (2025)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)
- [Minimizing Surrogate Losses for Decision-Focused Learning using Differentiable Optimization](https://mlsanity.com/paper/2508.11365/) (2025)
- [Prediction Loss Guided Decision-Focused Learning](https://mlsanity.com/paper/2509.08359/) (2025)

## Abstract (arXiv)

Many decision-making processes involve solving a combinatorial optimization problem with uncertain input that can be estimated from historic data. Recently, problems in this class have been successfully addressed via end-to-end learning approaches, which rely on solving one optimization problem for each training instance at every epoch. In this context, we provide two distinct contributions. First, we use a Noise Contrastive approach to motivate a family of surrogate loss functions, based on viewing non-optimal solutions as negative examples. Second, we address a major bottleneck of all predict-and-optimize approaches, i.e. the need to frequently recompute optimal solutions at training time. This is done via a solver-agnostic solution caching scheme, and by replacing optimization calls with a lookup in the solution cache. The method is formally based on an inner approximation of the feasible space and, combined with a cache lookup strategy, provides a controllable trade-off between training time and accuracy of the loss approximation. We empirically show that even a very slow growth rate is enough to match the quality of state-of-the-art methods, at a fraction of the computational cost.