Revisiting Decentralized Online Convex Optimization with Compressed Communication

Decentralized online convex optimization (D-OCO) is a popular framework for distributed applications with streaming data. To tackle the communication bottleneck, previous studies have investigated D-OCO with compressed communication and proposed several algorithms that are variants of online gradient descent (OGD). However, for D-OCO with exact communication, the best existing algorithms are variants of follow-the-regularized-leader (FTRL). In this paper, for the first time, we propose two FTRL-type algorithms for D-OCO with compressed communication. Compared with OGD-type algorithms, our algorithms are more elegant in both algorithmic design and theoretical analysis. The key insight is that the dual update mechanism of FTRL allows us to make a simple application of the technique for average consensus with communication compression. More specifically, our first algorithm considers the full-information setting, and can match the existing regret bounds. Our second algorithm is designed for the bandit setting, and can significantly improve both the regret bounds and communication costs of existing algorithms.