Gradient-free distributed online optimization in networks
Yuhang Liu
Wenxiao Zhao
Nan Zhang
Dongdong Lv
Shuai Zhang
Abstract：In this paper, we consider the distributed online optimization problem on a time-varying network, where each agent on the network has its own time-varying objective function and the goal is to minimize the overall loss accumulated. Moreover, we focus on distributed algorithms which do not use gradient information and projection operators to improve the applicability and computational efficiency. By introducing the deterministic differences and the randomized differences to substitute the gradient information of the objective functions and removing the projection operator in the traditional algorithms, we design two kinds of gradient-free distributed online optimization algorithms without projection step, which can economize considerable computational resources as well as has less limitations on the applicability. We prove that both of two algorithms achieves consensus of the estimates and regrets of O(log(T)) for local strongly convex objective, respectively. Finally, a simulation example is provided to verify the theoretical results.
Keywords：Distributed optimizationOnline convex optimizationGradient-free algorithmProjection-free algorithm
Publication Date：2025-05-30
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：14( 207-220 )