Distributed zeroth-order online optimization with communication delays

This paper investigates distributed online optimization in a networked multiagent system, where each agent has its own private objective and constraint functions that vary over time. In many real-world scenarios, computing the gradient of the cost function can be challenging, especially when agents have limited computational capabilities. Moreover, communication delays are common in practical networked systems due to various factors. This paper considers a unified framework for distributed online optimization that can handle bandit feedback and communication delays feedback simultaneously. A distributed primal-dual algorithm is proposed that utilizes bandit feedback, in which the agents estimate the gradients of their objective and constraint functions by sampling the function values. An enlarged network model that incorporates the delayed information exchanged among the agents is introduced. Through theoretical analysis, it is shown that the proposed algorithm achieves sublinear upper bounds on both the dynamic regret and the constraint violation despite communication delays.