Dynamic regret for decentralized online bandit gradient descent with local steps

Abstract

In this paper, we focus on a decentralized online convex optimization problem over a multi-agent system, where each agent is equipped with a time-varying objective function. To handle the communication bottleneck and reduce the communication costs, we consider the method of local steps, where the agents communicate with their neighbors after performing local gradient descent steps. Under bandit feedback, we develop the Local-Decentralized Online Bandit Gradient Descent (Local-DOBGD) algorithm, which combines local steps and gradient descent. The performance of the developed algorithm is analyzed and the dynamic regret bound $O\left(\sqrt{T(1+P_T)}\right)$ is obtained, which is concerned with time horizon $T$ and path-length $P_T$. Finally, we provide a numerical example to verify the effectiveness of the Local-DOBGD algorithm.