Distributed Online Optimization With Gradient-free Design

This paper studies an online optimization problem, where the cost function at every time stage is summation of a group of local cost functions assigned to to a single agent/node in a multi-agent network. We propose a distributed algorithm by combining the gradient descent method and consensus design. Then we prove that the regret of our online optimization algorithm as well as the accumulative disagreement for the multi-agent network is sublinear under a properly chosen stepsize.