Better scalability under potentially heavy-tailed gradients

Abstract: We study a scalable alternative to robust gradient descent (RGD) techniques that can be used when the gradients can be heavy-tailed, though this will be unknown to the learner. The core technique is simple: instead of trying to robustly aggregate gradients at each step, which is costly and leads to sub-optimal dimension dependence in risk bounds, we choose a candidate which does not diverge too far from the majority of cheap stochastic sub-processes run for a single pass over partitioned data. In addition to formal guarantees, we also provide empirical analysis of robustness to perturbations to experimental conditions, under both sub-Gaussian and heavy-tailed data. The result is a procedure that is simple to implement, trivial to parallelize, which keeps the formal strength of RGD methods but scales much better to large learning problems.