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：本文研究将机器学习预测建议融入覆盖网络，以使其拓扑结构适应动态请求需求。此类需求感知系统近来备受关注，例如在数据结构领域（Fu等人在ICLR 2025，Zeynali等人在ICML 2024）。本文将该理念拓展至覆盖网络场景，其中请求并非针对数据结构中的单个键值，而是发生在通信节点对之间，且算法需以分布式方式运行。在此设定下，我们提出一种算法，可动态调整覆盖网络的拓扑结构（及路由路径），以最小化比特传输的跳距，即距离与需求量的乘积。各节点以分布式方式接收（不可信的）未来需求预测，据此选择其邻居集合与转发表。本文聚焦于优化经典的跳表网络（SLNs），因其结构简洁。我们首先引入连续跳表网络（C-SLNs），这是专为容忍预测误差而设计的SLN泛化模型。随后提出名为LASLiN的学习增强算法，并证明其性能具有以下特性：（i）在预测准确时接近最优SLN（$O(1)$一致性）；（ii）在预测完全错误时与传统覆盖网络相比最多仅存在对数级差距（$O(\log^2 n)$鲁棒性，其中$n$为网络节点数）。最后，通过在合成数据与真实需求数据上模拟多种误差类型，验证了LASLiN对预测误差的适应能力（即其平滑性）。