A Proof of Theorem 1, A2, B1, B

A.1 Proof Sketch We first introduce the following lemma: Lemma 1. We first consider the condition number of Ĥ when X is in a locally convex area. In general, it is hard to develop a convergence rate for objective values. However, when the global model is in a locally convex area of f, we can obtain the relationship between the gradient and the local optimum. Theorem 4. When there is no parameter heat dispersion, and X is in a µ-strongly convex area of f We note that there is a difference between equation 18 and 21: for each client i, equation 18 involves all the parameters of the full model while equation 21 involves only partial parameters of the submodel, which causes a change in the lower bound of T (Y) and further leads to a change of conclusion.