Novel Gradient Sparsification Algorithm via Bayesian Inference

Error accumulation is an essential component of the Top-k sparsification method in distributed gradient descent. It implicitly scales the learning rate and prevents the slow-down of lateral movement, but it can also deteriorate convergence. This paper proposes a novel sparsification algorithm called regularized Top-k (RegTop-k) that controls the learning rate scaling of error accumulation. The algorithm is developed by looking at the gradient sparsification as an inference problem and determining a Bayesian optimal sparsification mask via maximum-a-posteriori estimation. It utilizes past aggregated gradients to evaluate posterior statistics, based on which it prioritizes the local gradient entries. Numerical experiments with ResNet-18 on CIFAR-10 show that at 0.1% sparsification, RegTop-k achieves about 8% higher accuracy than standard Top-k.