MPFlow: Learning Budgeted Max-Flow Optimization on the Lightning Network with Deep Graph Reinforcement Learning
For Lightning Network node operators, MPFlow provides a practical, deployed solution to maximize routing capacity under budget constraints, with real-world impact.
MPFlow uses deep graph reinforcement learning to solve budget-constrained max-flow optimization for liquidity placement in the Bitcoin Lightning Network, selecting k edge additions to maximize s-t max-flow. In production, it executed 4640 channel-open decisions allocating 267.3 BTC across 30 managed nodes, outperforming heuristic baselines.
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.