Communication Compression for Distributed Online Saddle Point Problem

The paper considers the saddle point problem within a distributed online framework, addressing the challenge of communication burden by exchanging compressed information and computations among neighboring agents. The objective is to identify the saddle point of the cumulative loss functions for all agents within discrete time intervals. The efficacy of the proposed algorithm is evaluated using dynamic regret as a metric. Two distinct distributed online algorithms are introduced to search for the saddle point. One algorithm operates with full-information feedback, while another utilizes bandit feedback. Both algorithms incorporate communication compression techniques. The paper provides simulation experimental results to illustrate the performance of these algorithms.