# Branch Ranking for Efficient Mixed-Integer Programming via Offline Ranking-based Policy Learning

arXiv: https://arxiv.org/abs/2207.13701 · HTML: https://mlsanity.com/paper/2207.13701/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 7 of its 21 references that are in the map.
- First posted on arXiv 26 Jul 2022.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 7 of 7)

- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Learning to Branch](https://mlsanity.com/paper/1803.10150/) (2018)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [Reinforcement Learning for Variable Selection in a Branch and Bound Algorithm](https://mlsanity.com/paper/2005.10026/) (2020)

## Built on by (most cited first, 2 of 2)

- [SORREL: Suboptimal-Demonstration-Guided Reinforcement Learning for Learning to Branch](https://mlsanity.com/paper/2412.15534/) (2024)
- [Discounted Pseudocosts in MILP](https://mlsanity.com/paper/2407.06237/) (2024)

## Abstract (arXiv)

Deriving a good variable selection strategy in branch-and-bound is essential for the efficiency of modern mixed-integer programming (MIP) solvers. With MIP branching data collected during the previous solution process, learning to branch methods have recently become superior over heuristics. As branch-and-bound is naturally a sequential decision making task, one should learn to optimize the utility of the whole MIP solving process instead of being myopic on each step. In this work, we formulate learning to branch as an offline reinforcement learning (RL) problem, and propose a long-sighted hybrid search scheme to construct the offline MIP dataset, which values the long-term utilities of branching decisions. During the policy training phase, we deploy a ranking-based reward assignment scheme to distinguish the promising samples from the long-term or short-term view, and train the branching model named Branch Ranking via offline policy learning. Experiments on synthetic MIP benchmarks and real-world tasks demonstrate that Branch Rankink is more efficient and robust, and can better generalize to large scales of MIP instances compared to the widely used heuristics and state-of-the-art learning-based branching models.