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

2026-07-09

AI Summary

This study addresses the problem of optimally opening payment channels in the Bitcoin Lightning Network under a fixed budget to maximize routing capacity. It formulates this challenge for the first time as a budget-constrained combinatorial optimization problem on graphs, specifically selecting k edges to maximize the s-t max-flow. The authors propose a graph reinforcement learning approach that integrates message-passing neural networks with the Proximal Policy Optimization (PPO) algorithm. To guide the agent toward capacity-aware decisions rather than merely connecting to high-degree hubs, they introduce action masking and a curriculum learning strategy that excludes central nodes during early training stages. Evaluated on real-world Lightning Network snapshots, the method significantly outperforms strong heuristic baselines and has been deployed in production, guiding 30 nodes to open 4,640 channels with a total capacity of 267.3 BTC (over $16 million).

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.

Problem

• liquidity placement
• Lightning Network
• max-flow
• budget-constrained optimization
• routing capacity

Innovation

• graph reinforcement learning
• max-flow optimization
• Lightning Network
• budget-constrained optimization
• message-passing neural network