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Federated learning (FL) algorithms usually sample a fraction of clients ineach round (partial participation) when the number of participants is large andthe server's communication bandwidth is limited. Recent works on theconvergence analysis of FL have focused on unbiased client sampling, e.g.,sampling uniformly at random, which suffers from slow wall-clock time forconvergence due to high degrees of system heterogeneity and statisticalheterogeneity. This paper aims to design an adaptive client sampling algorithmthat tackles both system and statistical heterogeneity to minimize thewall-clock convergence time. We obtain a new tractable convergence bound for FLalgorithms with arbitrary client sampling probabilities. Based on the bound, weanalytically establish the relationship between the total learning time andsampling probabilities, which results in a non-convex optimization problem fortraining time minimization. We design an efficient algorithm for learning theunknown parameters in the convergence bound and develop a low-complexityalgorithm to approximately solve the non-convex problem. Experimental resultsfrom both hardware prototype and simulation demonstrate that our proposedsampling scheme significantly reduces the convergence time compared to severalbaseline sampling schemes. Notably, our scheme in hardware prototype spends 73%less time than the uniform sampling baseline for reaching the same target loss.

Tackling System and Statistical Heterogeneity for Federated Learning with Adaptive Client Sampling