Title: FedGSNR: Accelerating Federated Learning on Non-IID Data via Maximum Gradient Signal to Noise Ratio. Abstract: Federated learning (FL) allows participants jointly training a model without direct data sharing. In such a process, participants rather than the central server perform local updates of stochastic gradient descent (SGD) and the central server aggregates the gradients from the participants to update the global model. However, the non-iid training data in participants significantly impact global model convergence.Most of existing studies addressed this issue by utilizing variance reduction or regularization. However, these studies focusing on specific datasets lack theoretical guarantee for efficient model training. In this paper, we provide a novel perspective on the non-iid issue by optimizing Gradient Signal to Noise Ratio (GSNR) during model training. In each participant, we decompose local gradients calculated on the non-iid training data into the signal and noise components and then speed up the model convergence by maximizing GSNR. We prove that GSNR can be maximized by using the optimal number of local updates. Subsequently, we develop FedGSNR to compute the optimal number of local updates for each participant, which can be applied to existing gradient calculation algorithms to accelerate the global model convergence. Moreover, according to the positive correlation between GSNR and the quality of shared information, FedGSNR allows the server to accurately evaluate contributions of different participants (i.e., the quality of local datasets) by utilizing GSNR. Extensive experimental evaluations demonstrate that FedGSNR achieves on average a 1.69× speedup with comparable accuracy.