Building on top of blockchain, payment channel networks-backed (PCNs) cryptocurrencies emerge as a promising solution for a mobile payment system with fewer intermediaries, more security, higher speed, and lower cost. A key problem for PCN is payment channel rebalancing, that is, finding a set of circular transactions that restore a PCN with skewed channel balances back into an equilibrium state. However, existing practice on payment channel rebalancing either has a hard limit on the problem size or tends to fall into local optimum. To address these challenges, we propose DRL-PCR, aDeepReinforcementLearning-basedPaymentChannelRebalancing algorithm. On one hand, DRL-PCR leverages the strong approximation ability of deep neural networks to handle large problem spaces. On the other hand, DRL-PCR decomposes the rebalancing problem into a sequence of decision-making problems and progressively builds the final solution. By aiming to find a globally optimized solution and solving the long-term optimization model of DRL, DRL-PCR is superior to greedy-based algorithms and can mitigate the risk of getting trapped in a local optimum. In particular, payment channel rebalancing typically involves dealing with graph-structured data, where the major obstacle lies in understanding the sophisticated circular dependencies between payment channels and routing paths. DRL-PCR achieves this by encoding the input data with a novel graph neural network-based model and capturing the circular dependencies through a customized message passing process. In addition, considering the distributed nature of PCN, DRL-PCR uses a leadership election protocol to elect leaders for decision-making. Evaluations on the historical data of two real-world PCNs demonstrate that DRL-PCR can restore the PCN to a more balanced state and improve the transaction throughput and success ratios by up to 2.1x and 1.6x, respectively.

Payment channel networks (PCNs) are considered as a prominent solution for scaling blockchain, where users can establish payment channels and complete transactions in an off-chain manner. However, it is non-trivial to schedule transactions in PCNs and most existing routing algorithms suffer from the following challenges: 1) one-shot optimization, 2) privacy-invasive channel probing, 3) vulnerability to DoS attacks. To address these challenges, we propose a privacy-aware transaction scheduling algorithm with defence against DoS attacks based on deep reinforcement learning (DRL), namely PTRD. Specifically, considering both the privacy preservation and long-term throughput into the optimization criteria, we formulate the transaction-scheduling problem as a Constrained Markov Decision Process. We then design PTRD, which extends off-the-shelf DRL algorithms to constrained optimization with an additional cost critic-network and an adaptive Lagrangian multiplier. Moreover, considering the distribution nature of PCNs, in which each user schedules transactions independently, we develop a distributed training framework to collect the knowledge learned by each agent so as to enhance learning effectiveness. With the customized network design and the distributed training framework, PTRD achieves a good balance between the optimization of the throughput and the minimization of privacy risks. Evaluations show that PTRD outperforms the state-of-the-art PCN routing algorithms by 2.7%–62.5% in terms of the long-term throughput while satisfying privacy constraints.

Blockchain-based cryptocurrencies have developed rapidly in recent years, however, scalability is one of the biggest challenge. Payment channel networks (PCNs) are one of the important solutions to blockchain scalability and routing is the most critical problem in PCN. Routing algorithms in PCNs have evolved fast and achieved high throughput. However, most of these routing algorithms are designed from the perspective of technical feasibility, and few algorithms focus on the incentives of each off-chain participant, especially the economic incentives for intermediate routing nodes. Besides, due to the highly dynamic nature of off-chain channel deposits, existing routing algorithms rely heavily on channel deposit probing in order to ensure high throughput. In this article, we design routing algorithms from an incentive perspective to improve the profit of intermediate nodes and use deep learning to reduce the dependency of off-chain routing on channel deposit probing. Our experiments show that under the same model, MDRL-IR can increase the profit of intermediate nodes by up to 1.87x and increase the throughput by up to 2.0x compared to the state-of-the-art routing algorithm, while ensuring that the user routing cost per unit throughput remains unchanged. Moreover, approximate performance can be achieved when deposit probing is greatly reduced.