Asynchronous Zeroth-Order Distributed Optimization with Residual Feedback

We consider a zeroth-order distributed optimization problem, where the global objective function is a black-box function and, as such, its gradient information is inaccessible to the local agents. Instead, the local agents can only use the values of the objective function to estimate the gradient and update their local decision variables. In this paper, we also assume that these updates are done asynchronously. To solve this problem, we propose an asynchronous zeroth-order distributed optimization method that relies on a one-point residual feedback to estimate the unknown gradient. We show that this estimator is unbiased under asynchronous updating, and theoretically analyze the convergence of the proposed method. We also present numerical experiments that demonstrate that our method outperforms two-point methods under asynchronous updating. To the best of our knowledge, this is the first asynchronous zeroth-order distributed optimization method that is also supported by theoretical guarantees.