Alyazeed Albasyoni

Alyazeed Albasyoni, Mher Safaryan, Laurent Condat et al.

Communicating information, like gradient vectors, between computing nodes in distributed and federated learning is typically an unavoidable burden, resulting in scalability issues. Indeed, communication might be slow and costly. Recent advances in communication-efficient training algorithms have reduced this bottleneck by using compression techniques, in the form of sparsification, quantization, or low-rank approximation. Since compression is a lossy, or inexact, process, the iteration complexity is typically worsened; but the total communication complexity can improve significantly, possibly leading to large computation time savings. In this paper, we investigate the fundamental trade-off between the number of bits needed to encode compressed vectors and the compression error. We perform both worst-case and average-case analysis, providing tight lower bounds. In the worst-case analysis, we introduce an efficient compression operator, Sparse Dithering, which is very close to the lower bound. In the average-case analysis, we design a simple compression operator, Spherical Compression, which naturally achieves the lower bound. Thus, our new compression schemes significantly outperform the state of the art. We conduct numerical experiments to illustrate this improvement.

Motasem Alfarra, Slavomir Hanzely, Alyazeed Albasyoni et al.

Recent advances in the theoretical understanding of SGD led to a formula for the optimal batch size minimizing the number of effective data passes, i.e., the number of iterations times the batch size. However, this formula is of no practical value as it depends on the knowledge of the variance of the stochastic gradients evaluated at the optimum. In this paper we design a practical SGD method capable of learning the optimal batch size adaptively throughout its iterations for strongly convex and smooth functions. Our method does this provably, and in our experiments with synthetic and real data robustly exhibits nearly optimal behaviour; that is, it works as if the optimal batch size was known a-priori. Further, we generalize our method to several new batch strategies not considered in the literature before, including a sampling suitable for distributed implementations.