# Branch & Learn with Post-hoc Correction for Predict+Optimize with Unknown Parameters in Constraints

arXiv: https://arxiv.org/abs/2303.06698 · HTML: https://mlsanity.com/paper/2303.06698/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 12 Mar 2023.

## Builds on (most cited first, 6 of 6)

- [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)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization](https://mlsanity.com/paper/2006.01610/) (2020)
- [Predict+Optimize for Packing and Covering LPs with Unknown Parameters in Constraints](https://mlsanity.com/paper/2209.03668/) (2022)
- [Branch & Learn for Recursively and Iteratively Solvable Problems in Predict+Optimize](https://mlsanity.com/paper/2205.01672/) (2022)

## Built on by (most cited first, 5 of 5)

- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning](https://mlsanity.com/paper/2307.05213/) (2023)
- [Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints](https://mlsanity.com/paper/2510.04951/) (2025)
- [Learning From Scenarios for Stochastic Repairable Scheduling](https://mlsanity.com/paper/2312.03492/) (2023)
- [Scalable Decision Focused Learning via Online Trainable Surrogates](https://mlsanity.com/paper/2512.03861/) (2025)

## Abstract (arXiv)

Combining machine learning and constrained optimization, Predict+Optimize tackles optimization problems containing parameters that are unknown at the time of solving. Prior works focus on cases with unknowns only in the objectives. A new framework was recently proposed to cater for unknowns also in constraints by introducing a loss function, called Post-hoc Regret, that takes into account the cost of correcting an unsatisfiable prediction. Since Post-hoc Regret is non-differentiable, the previous work computes only its approximation. While the notion of Post-hoc Regret is general, its specific implementation is applicable to only packing and covering linear programming problems. In this paper, we first show how to compute Post-hoc Regret exactly for any optimization problem solvable by a recursive algorithm satisfying simple conditions. Experimentation demonstrates substantial improvement in the quality of solutions as compared to the earlier approximation approach. Furthermore, we show experimentally the empirical behavior of different combinations of correction and penalty functions used in the Post-hoc Regret of the same benchmarks. Results provide insights for defining the appropriate Post-hoc Regret in different application scenarios.