# Influence branching for learning to solve mixed-integer programs online

arXiv: https://arxiv.org/abs/2510.04273 · HTML: https://mlsanity.com/paper/2510.04273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 19 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Learning to Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (2021)
- [DASH: Dynamic Approach for Switching Heuristics](https://mlsanity.com/paper/1307.4689/) (2013)
- [Branch and Bound in Mixed Integer Linear Programming Problems: A Survey of Techniques and Trends](https://mlsanity.com/paper/2111.06257/) (2021)
- [Online Learning for Scheduling MIP Heuristics](https://mlsanity.com/paper/2304.03755/) (2023)
- [The MIP Workshop 2023 Computational Competition on Reoptimization](https://mlsanity.com/paper/2311.14834/) (2023)

## Abstract (arXiv)

On the occasion of the 20th Mixed Integer Program Workshop's computational competition, this work introduces a new approach for learning to solve MIPs online. Influence branching, a new graph-oriented variable selection strategy, is applied throughout the first iterations of the branch and bound algorithm. This branching heuristic is optimized online with Thompson sampling, which ranks the best graph representations of MIP's structure according to computational speed up over SCIP. We achieve results comparable to state of the art online learning methods. Moreover, our results indicate that our method generalizes well to more general online frameworks, where variations in constraint matrix, constraint vector and objective coefficients can all occur and where more samples are available.