Better scalability under potentially heavy-tailed feedback

TL;DR

This paper introduces scalable robust gradient descent methods that efficiently handle heavy-tailed data by focusing on robust candidate selection, improving scalability and robustness in large-scale learning tasks.

Contribution

It proposes a new approach that replaces costly gradient aggregation with a robust candidate selection process, enhancing scalability and robustness for heavy-tailed data.

Findings

Method scales better to large problems.

Empirical robustness to heavy-tailed noise.

Applicable to various benchmark datasets.

Abstract

We study scalable alternatives to robust gradient descent (RGD) techniques that can be used when the losses and/or 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 instead focus computational effort on robustly choosing (or newly constructing) a strong candidate based on a collection of cheap stochastic sub-processes which can be run in parallel. The exact selection process depends on the convexity of the underlying objective, but in all cases, our selection technique amounts to a robust form of boosting the confidence of weak learners. 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, along with applications to a variety of benchmark datasets. The overall take-away is an extensible procedure that is simple to implement, trivial to parallelize, which keeps the formal merits of RGD methods but scales much better to large learning problems.