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Federated learning (FL), as an emerging edge artificial intelligence paradigm, enables many edge devices to collaboratively train a global model without sharing their private data. To enhance the training efficiency of FL, various algorithms have been proposed, ranging from first-order to second-order methods. However, these algorithms cannot be applied in scenarios where the gradient information is not available, e.g., federated black-box attack and federated hyperparameter tuning. To address this issue, in this paper we propose a derivative-free federated zeroth-order optimization (FedZO) algorithm featured by performing multiple local updates based on stochastic gradient estimators in each communication round and enabling partial device participation. Under non-convex settings, we derive the convergence performance of the FedZO algorithm on non-independent and identically distributed data and …