Distributed Zeroth-order Optimization Over Directed Graphs

This paper investigates the problem of distributed optimization over a directed graph. Additionally, each agent can only get zeroth-order (ZO) information of its objective function. The objective is to minimize the sum of the local cost functions without gradient information of the objective function. A novel distributed zeroth-order algorithm is developed over directed graphs based on the gradient estimator. The proposed algorithm is theoretically analyzed and shown to achieve linear convergence to a neighborhood of the optimal solution under strong convexity and smoothness assumptions. A key feature of the algorithm design is that it removes the dependence on the gradient of the objective function. The proposed algorithm are compared through numerical experiments on various datasets.