Decentralized Online Optimization With Compressed Communication Over Directed Graphs

This article focuses on a decentralized online optimization problem over multiagent systems, where the interactions are modeled by a strongly connected directed graph. The objective of each agent is to minimize the global loss function accumulated by all agents' local loss functions, which are time-varying and only known by themselves. To address the communication bottleneck caused by the high-dimensional data and large-scale networks, we design a decentralized online algorithm with compressed communication, decentralized online gradient push-sum with compressed communication (CC-DOGPS). For strongly convex functions, a sublinear regret bound $\mathcal {O}((\ln T)^{2})$ of our designed algorithm is obtained, where $T$ is the time horizon. Finally, two numerical simulations are given to validate the theoretical results and illustrate the efficiency of our designed algorithm.