Adaptive Batch Size Time Evolving Stochastic Gradient Descent for Federated Learning

Variance reduction has been shown to improve the performance of Stochastic Gradient Descent (SGD) in centralized machine learning. However, when it is extended to federated learning systems, many issues may arise, including (i) mega-batch size settings; (ii) additional noise introduced by the gradient difference between the current iteration and the snapshot point; and (iii) gradient (statistical) heterogeneity. In this paper, we propose a lightweight algorithm termed federated adaptive batch size time evolving variance reduction (FedATEVR) to tackle these issues, consisting of an adaptive batch size setting scheme and a time-evolving variance reduction gradient estimator. In particular, we use the historical gradient information to set an appropriate mega-batch size for each client, which can steadily accelerate the local SGD process and reduce the computation cost. The historical information involves both global and local gradient, which mitigates unstable varying in mega-batch size introduced by gradient heterogeneity among the clients. For each client, the gradient difference between the current iteration and the snapshot point is used to tune the time-evolving weight of the variance reduction term in the gradient estimator. This can avoid meaningless variance reduction caused by the out-of-date snapshot point gradient. We theoretically prove that our algorithm can achieve a linear speedup of of $\mathcal {O}(\frac{1}{\sqrt{SKT}})$ for non-convex objective functions under partial client participation. Extensive experiments demonstrate that our proposed method can achieve higher test accuracy than the baselines and decrease communication rounds greatly.