Paper Detail
Harrison Rush, Vincent Davis, Simone Antonelli, Vikash Singh, Jesse Shrader, Emanuele Rossi
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.
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@article{rush2026mpflow,
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},
year = {2026},
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 (P},
url = {https://arxiv.org/abs/2607.08703},
keywords = {cs.LG},
eprint = {2607.08703},
archiveprefix = {arXiv},
}
{}