This paper studies the integration of machine-learned advice in overlay networks in order to adapt their topology to the incoming demand. Such demand-aware systems have recently received much attention, for example in the context of data structures (Fu et al. in ICLR 2025, Zeynali et al. in ICML 2024). We in this paper extend this vision to overlay networks where requests are not to individual keys in a data structure but occur between communication pairs, and where algorithms have to be distributed. In this setting, we present an algorithm that adapts the topology (and the routing paths) of the overlay network to minimize the hop distance travelled by bit, that is, distance times demand. In a distributed manner, each node receives an (untrusted) prediction of the future demand to help him choose its set of neighbors and its forwarding table. This paper focuses on optimizing the well-known skip list networks (SLNs) for their simplicity. We start by introducing continuous skip list networks (C-SLNs) which are a generalization of SLNs specifically designed to tolerate predictive errors. We then present our learning-augmented algorithm, called LASLiN, and prove that its performance is (i) similar to the best possible SLN in case of good predictions ($O(1)$-consistency) and (ii) at most a logarithmic factor away from a standard overlay network in case of arbitrarily wrong predictions ($O(\log^2 n)$-robustness, where $n$ is the number of nodes in the network). Finally, we demonstrate the resilience of LASLiN against predictive errors (ie, its smoothness) using various error types on both synthetic and real demands.

翻译：本文研究了机器学习建议在覆盖网络中的集成，以使其拓扑结构适应传入需求。这类需求感知系统最近受到广泛关注，例如在数据结构的背景下（Fu 等人在 ICLR 2025，Zeynali 等人在 ICML 2024）。本文将此理念扩展到覆盖网络，其中请求并非针对数据结构中的单个键，而是发生在通信对之间，并且算法必须分布运行。在此设置中，我们提出了一种算法，能够自适应调整覆盖网络的拓扑结构（以及路由路径），以最小化每个比特的跳距离，即距离与需求的乘积。以分布式方式，每个节点接收对未来需求的（不可信）预测，以帮助其选择邻居集和转发表。本文专注于优化众所周知的跳表网络（SLN）的简洁性。我们首先引入连续跳表网络（C-SLN），它是 SLN 的一种泛化，专门设计用于容忍预测误差。然后，我们提出名为 LASLiN 的学习增强算法，并证明其性能：（i）在预测良好时与最优 SLN 相近（$O(1)$-一致性），（ii）在预测任意错误时，与标准覆盖网络相比最多相差对数因子（$O(\log^2 n)$-鲁棒性，其中 $n$ 是网络节点数）。最后，我们通过在合成和真实需求上使用多种误差类型，展示了 LASLiN 对预测误差的鲁棒性（即其平滑性）。