Title: A Learning-Augmented Overlay Network
Primary area: optimization
Keywords: learning-augmented algorithms, peer-to-peer protocol, dynamic system, skip list

Abstract: This paper studies the integration of machine-learned advice in overlay networks to improve the overall connectivity. Our algorithms are based on Skip List Networks (SLN), which is natural extension of skip lists that supports pairwise communication. In particular our work goes beyond learning-augmented single-source skip lists (studied recently in ICLR 2025 by Fu et al. and ICML 2024 by Zeynali et al., considering a prediction model where each node of the network individually receives a local prediction of its future communications to the rest of network. We utilize this model to develop a distributed, learning-augmented SLN to optimize the serving of any weighted pairwise demand.

We first solve the optimization problem of finding an optimal SLN given a certain demand, which we show is polynomial with a dynamic programming approach. We then introduce a novel network structure called Continuous SLN, where the heights of each node is relaxed to be any real number. Finally, we show how a random, uniform noise on top of each node's height makes the network robust against any predictions, even adversarial, while the performances are kept unchanged when the predictions are desired. Concretely, adversarial predictions can cause our network to be a logarithmic factor away from any optimal network without prediction. Furthermore, we show that, for highly sparse demands, a refined version of our algorithm shows no drawbacks in asymptotics for any prediction and presents exponential improvements when the predictions are good. Finally, we empirically show that our learning-augmented overlay network demonstrate resistance against small error with evaluations on synthetic and real-world data-sets.

TL;DR: A peer-to-peer network with improved connectivity performances in case of correct traffic predictions and still performances guarantees when the predictions are arbitrary.