One‐Point Residual Feedback Algorithms for Distributed Online Convex and Non‐Convex Optimization

ABSTRACT This paper primarily addresses the distributed online optimization problem where the objective functions are assumed to be convex or non‐convex. First, two distributed algorithms are proposed to solve the convex and non‐convex optimization problem, where the one‐point residual feedback technology is introduced to estimate the gradient of local objective functions. Then the regret bounds of proposed algorithms are derived respectively under the assumption that the local objective functions are Lipschitz or smooth, which implies that the regrets are sublinear. Finally, we give two numerical examples of distributed convex optimization and distributed resource allocation problems to show the effectiveness of the proposed algorithms.