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Federated Learning (FL) is a distributed machine learning framework toalleviate the data silos, where decentralized clients collaboratively learn aglobal model without sharing their private data. However, the clients'Non-Independent and Identically Distributed (Non-IID) data negatively affectthe trained model, and clients with different numbers of local updates maycause significant gaps to the local gradients in each communication round. Inthis paper, we propose a Federated Vectorized Averaging (FedVeca) method toaddress the above problem on Non-IID data. Specifically, we set a novelobjective for the global model which is related to the local gradients. Thelocal gradient is defined as a bi-directional vector with step size anddirection, where the step size is the number of local updates and the directionis divided into positive and negative according to our definition. In FedVeca,the direction is influenced by the step size, thus we average thebi-directional vectors to reduce the effect of different step sizes. Then, wetheoretically analyze the relationship between the step sizes and the globalobjective, and obtain upper bounds on the step sizes per communication round.Based on the upper bounds, we design an algorithm for the server and the clientto adaptively adjusts the step sizes that make the objective close to theoptimum. Finally, we conduct experiments on different datasets, models andscenarios by building a prototype system, and the experimental resultsdemonstrate the effectiveness and efficiency of the FedVeca method.

FedVeca: Federated Vectorized Averaging on Non-IID Data with Adaptive Bi-directional Global Objective