Decentralized Online Strongly Convex Optimization with General Compressors and Random Disturbances

This paper considers the decentralized online strongly convex optimization over a multi-agent network, where the objective is to minimize a global loss function accumulated by the local loss functions of all agents. The Time-Varying Scaling Compression method is applied to deal with the communication bottleneck in the presence of disturbances. Then, by using the scaling compression, a decentralized online algorithm is proposed and the convergence results of the algorithm are analyzed. By choosing proper parameters, a sublinear regret can be obtained, which matches the same order as those of algorithms with no disturbances. Finally, numerical simulations are given to demonstrate the efficiency of the proposed algorithm.