{"ID":6267294,"CreatedAt":"2026-07-10T01:11:38.759438437Z","UpdatedAt":"2026-07-13T01:02:08.706470581Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.08703","arxiv_id":"2607.08703","title":"MPFlow: Learning Budgeted Max-Flow Optimization on the Lightning Network with Deep Graph Reinforcement Learning","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.","short_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-ground...","url_abs":"https://arxiv.org/abs/2607.08703","url_pdf":"https://arxiv.org/pdf/2607.08703v1","authors":"[\"Harrison Rush\",\"Vincent Davis\",\"Simone Antonelli\",\"Vikash Singh\",\"Jesse Shrader\",\"Emanuele Rossi\"]","published":"2026-07-09T17:09:20Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Reinforcement Learning\"]","has_code":false}