Gradient-free algorithms for distributed online convex optimization

In this paper, we consider the distributed bandit convex optimization of time-varying objective functions over a network. By introducing perturbations into the objective functions, we design a deterministic difference and a randomized difference to replace the gradient information of the objective functions and propose two classes of gradient-free distributed algorithms. We prove that both the two classes of algorithms achieve regrets of O(T-3/4) for convex objective functions and O(T-2/3) for strongly convex objective functions, with respect to the time index T and consensus of the estimates established as well. Simulation examples are given justifying the theoretical results.