MPFlow: Learning Budgeted Max-Flow Optimization on the Lightning Network with Deep Graph Reinforcement Learning

Harrison Rush; Vincent Davis; Simone Antonelli; Vikash Singh; Jesse Shrader; Emanuele Rossi

MPFlow: Learning Budgeted Max-Flow Optimization on the Lightning Network with Deep Graph Reinforcement Learning

Machine Learning 2026-07-09 v1

Authors: Harrison Rush , Vincent Davis , Simone Antonelli , Vikash Singh , Jesse Shrader , Emanuele Rossi

Abstract

We address liquidity placement in the Bitcoin Lightning Network (LN): given a fixed budget, which channels should a node open to maximize its routing capacity? We cast this as a budget-constrained combinatorial optimization problem on graphs, selecting $k$ edge additions that maximize $s$ -- $t$ max-flow, a theory-grounded measure of routing capacity, and solve it with graph reinforcement learning. Our lightweight agent combines a message-passing policy network with proximal policy optimization (PPO) and action masking, and is trained under a hub-exclusion curriculum: the network's top hubs are removed from training subgraphs, forcing the policy to learn capacity-aware placement rather than hub attachment. In extensive experiments on real Lightning Network snapshots, our method consistently outperforms strong heuristic baselines on the max-flow objective across multiple seeds and unseen graphs. The agent has been deployed in production for peer recommendations, executing 4640 channel-open decisions that cumulatively allocate 267.3 BTC over $16 million across 30 managed nodes.

Cite

@article{arxiv.2607.08703,
  title  = {MPFlow: Learning Budgeted Max-Flow Optimization on the Lightning Network with Deep Graph Reinforcement Learning},
  author = {Harrison Rush and Vincent Davis and Simone Antonelli and Vikash Singh and Jesse Shrader and Emanuele Rossi},
  journal= {arXiv preprint arXiv:2607.08703},
  year   = {2026}
}