Variance Reduced ProxSkip: Algorithm, Theory and Application to Federated Learning
This work addresses communication bottlenecks in federated learning by improving local training methods, representing an incremental advance in the field.
The paper tackles the problem of communication efficiency in distributed optimization by enhancing local training methods with variance reduction, showing that their approach can be substantially faster in total training cost than the state-of-the-art ProxSkip method when local computation is expensive, with theoretical and empirical confirmation.
We study distributed optimization methods based on the {\em local training (LT)} paradigm: achieving communication efficiency by performing richer local gradient-based training on the clients before parameter averaging. Looking back at the progress of the field, we {\em identify 5 generations of LT methods}: 1) heuristic, 2) homogeneous, 3) sublinear, 4) linear, and 5) accelerated. The 5${}^{\rm th}$ generation, initiated by the ProxSkip method of Mishchenko, Malinovsky, Stich and Richtárik (2022) and its analysis, is characterized by the first theoretical confirmation that LT is a communication acceleration mechanism. Inspired by this recent progress, we contribute to the 5${}^{\rm th}$ generation of LT methods by showing that it is possible to enhance them further using {\em variance reduction}. While all previous theoretical results for LT methods ignore the cost of local work altogether, and are framed purely in terms of the number of communication rounds, we show that our methods can be substantially faster in terms of the {\em total training cost} than the state-of-the-art method ProxSkip in theory and practice in the regime when local computation is sufficiently expensive. We characterize this threshold theoretically, and confirm our theoretical predictions with empirical results.