Online Distributed Zeroth-Order Optimization With Non-Zero-Mean Adverse Noises

Abstract: In this paper, the problem of online distributed zeroth-order optimization subject to a set constraint is studied via a multi-agent network, where each agent can communicate with its immediate neighbors via a time-varying directed graph. Different from the existing works on online distributed zeroth- order optimization, we consider the case where the estimate on the gradients are influenced by some non-zero-mean adverse noises. To handle this problem, we propose a new online dis- tributed zeroth-order mirror descent algorithm involving a kernel function-based estimator and a clipped strategy. Particularly, in the estimator, the kernel function-based strategy is provided to deal with the adverse noises, and eliminate the low-order terms in the Taylor expansions of the objective functions. Furthermore, the performance of the presented algorithm is measured by employing the dynamic regrets, where the offline benchmarks are to find the optimal point at each time. Under the mild assumptions on the graph and the objective functions, we prove that if the variation in the optimal point sequence grows at a certain rate, then the high probability bound of the dynamic regrets increases sublinearly. Finally, a simulation experiment is worked out to demonstrate the effectiveness of our theoretical results.