Appendix for " Fine-Grained Theoretical Analysis of Federated Zeroth-Order Optimization "

The main notations of this paper are summarized in Table 1. Table 1: Descriptions of the main notations used in this work.Notations Descriptions N, n the total number of clients and the total sample number of each client S, S We first introduce the lemmas which will be used in our proofs. Let e be the base of the natural logarithm. The stated result in Part (b) is proved. The optimization bound is given.