# Scalable Decision-Focused Learning through Cost-Sensitive Regression

arXiv: https://arxiv.org/abs/2605.18005 · HTML: https://mlsanity.com/paper/2605.18005/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 14 of 14)

- [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)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimize](https://mlsanity.com/paper/2305.16830/) (2023)
- [Differentiating Through Integer Linear Programs with Quadratic Regularization and Davis-Yin Splitting](https://mlsanity.com/paper/2301.13395/) (2023)
- [Solver-Free Decision-Focused Learning for Linear Optimization Problems](https://mlsanity.com/paper/2505.22224/) (2025)
- [CaVE: A Cone-Aligned Approach for Fast Predict-then-optimize with Binary Linear Programs](https://mlsanity.com/paper/2312.07718/) (2023)
- [A Note on Task-Aware Loss via Reweighing Prediction Loss by Decision-Regret](https://mlsanity.com/paper/2211.05116/) (2022)
- [Learning Joint Models of Prediction and Optimization](https://mlsanity.com/paper/2409.04898/) (2024)
- [Sufficient Decision Proxies for Decision-Focused Learning](https://mlsanity.com/paper/2505.03953/) (2025)

## Abstract (arXiv)

Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These `predict-then-optimize' or `contextual optimization' problems have gained significant attention: end-to-end training methods can now minimize the downstream task cost rather than the predictive error. However, despite their effectiveness, these decision-focused learning (DFL) approaches often rely on repeated solving of the underlying combinatorial optimization problem during training, making them computationally expensive and difficult to scale. We reframe the learning problem as a cost-sensitive multi-output regression problem: multi-output due to the combinatorial problem having multiple uncertain parameters, and cost-sensitive due to the downstream task cost being the real target. Our technical contribution is the formalization of multiple loss function components that follow from this reframing: cost-insensitive normalization, decision-aware asymmetric penalization of over- and underpredictions, and instance-based costs that mimic the true downstream task-based loss locally. These components require zero or one solve per training data instance, while requiring no further solves during training. Experiments show that the combination of loss components achieves comparable downstream task quality to the state of the art, while being significantly more efficient, enabling scaling to problem sizes that have not been tackled before with DFL.