Tighter Regret Analysis and Optimization of Online Federated Learning

In federated learning (FL), it is generally assumed that all data are placed at clients in the beginning of machine learning (ML) optimization (i.e., offline learning). However, in many real-world applications, ML tasks are expected to proceed in an online fashion, wherein data samples are generated as a function of time and each client has to predict a label (or make a decision) upon receiving an incoming data. To this end, online FL (OFL) has been introduced, which aims at learning a sequence of global models from distributed streaming data such that a cumulative regret is minimized. In this framework, the vanilla method (named FedOGD) by combining online gradient descent and model averaging, which is regarded as the counterpart of FedSGD in the standard FL. Despite its asymptotic optimality, FedOGD suffers from high communication costs. In this paper, we present a communication-efficient OFL method by means of intermittent transmission (enabled by client subsampling and periodic transmission) and gradient quantization. For the first time, we derive the regret bound which can reflect the impact of data-heterogeneity and communication-efficient techniques. Based on our tighter analysis, we optimize the key parameters of OFedIQ such as sampling rate, transmission period, and quantization bits. Also, we prove that the optimized OFedIQ asymptotically achieves the performance of FedOGD while reducing the communication costs by 99%. Via experiments with real datasets, we validate the effectiveness of our algorithm on various online ML tasks.