Distributed online convex optimization with a bandit primal-dual mirror descent push-sum algorithm

Abstract

The distributed online convex optimization problem with time-varying constraints for multi-agent networks is addressed in this article. The purpose is to optimize a sequence of time-varying global cost functions defined as the accumulated values of local cost functions, also attempt to meet the requirement of a sequence of time-varying coupled constraint functions which denote the sum of local constraint functions. Cost functions and constraint functions are unknown to agents beforehand. It is supposed that each agent in the network communicates with its neighbours through a uniformly strongly connected sequence of time-varying directed communication topologies. This paper proposes the bandit distributed primal-dual mirror descent push-sum (BDPDMDPS) algorithm constructed by bandit primal-dual, mirror descent and push-sum methods. Operational performance of the presented algorithm is measured by expected regret and expected constraint violation, both of which are proved to be sublinear with respect to the total iteration span T in this paper. Finally, a numerical simulation example is shown, which confirms the results for expected regret and expected constraint violation of BDPDMDPS algorithm.