mlsanityData to 14 Oct 2026

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

arXiv 2607.08703 ↗First posted 9 Jul 2026cs.LGcited by 0

On the map: Deep reinforcement learning methods → Adversarial robustness and RL in finance

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods. Builds on 13 of its 27 references that are in the map. First posted on arXiv 9 Jul 2026.

Builds on

13 of 27 references.

References · 13

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  4. 2015Continuous control with deep reinforcement learningcited by 3,407
  5. 2016Asynchronous Methods for Deep Reinforcement Learningcited by 2,258
  6. 2017Learning Combinatorial Optimization Algorithms over Graphscited by 561
  7. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 310
  8. 2021Neural Algorithmic Reasoningcited by 94
  9. 2019Flash: Efficient Dynamic Routing for Offchain Networkscited by 5
  10. 2021Optimally Reliable & Cheap Payment Flows on the Lightning Networkcited by 3
  11. 2022Graph Neural Network Based Node Deployment for Throughput Enhancementcited by 3
  12. 2024Channel Balance Interpolation in the Lightning Network via Machine Learningcited by 3
1 more
  1. 2021Security and Privacy of Lightning Network Payments with Uncertain Channel Balancescited by 2

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  1. 2024Joint Combinatorial Node Selection and Resource Allocations in the Lightning Network using Attention-based Reinforcement Learning
  2. 2026Learning to Optimize: Joint Routing and Flow Allocation on Sparse Non-Euclidean Networks
  3. 2025RL-Exec: Impact-Aware Reinforcement Learning for Opportunistic Optimal Liquidation, Outperforms TWAP and a Book-Liquidity VWAP on BTC-USD Replays
  4. 2024Learning Sub-Second Routing Optimization in Computer Networks requires Packet-Level Dynamics
  5. 2024An Efficient Learning-based Solver Comparable to Metaheuristics for the Capacitated Arc Routing Problem
  6. 2026RAmmStein: Regime Adaptation in Mean-reverting Markets with Stein Thresholds -- Optimal Impulse Control in Concentrated AMMs
  7. 2025PoGO: A Scalable Proof of Useful Work via Quantized Gradient Descent and Merkle Proofs
  8. 2025Improving DeFi Accessibility through Efficient Liquidity Provisioning with Deep Reinforcement Learning