Improved scalability under heavy tails, without strong convexity

TL;DR

This paper introduces a scalable, robust algorithm for machine learning that effectively handles heavy-tailed data without relying on strong convexity, improving dimension dependence and providing transparent guarantees.

Contribution

It presents a simple robust validation sub-routine that enhances gradient-based methods for heavy-tailed data, avoiding expensive robustification steps and strong convexity assumptions.

Findings

Improved dimension dependence in risk bounds and computational cost.

The proposed method outperforms naive cross-validation under heavy tails.

Provides transparent guarantees for heavy-tailed data scenarios.

Abstract

Real-world data is laden with outlying values. The challenge for machine learning is that the learner typically has no prior knowledge of whether the feedback it receives (losses, gradients, etc.) will be heavy-tailed or not. In this work, we study a simple algorithmic strategy that can be leveraged when both losses and gradients can be heavy-tailed. The core technique introduces a simple robust validation sub-routine, which is used to boost the confidence of inexpensive gradient-based sub-processes. Compared with recent robust gradient descent methods from the literature, dimension dependence (both risk bounds and cost) is substantially improved, without relying upon strong convexity or expensive per-step robustification. Empirically, we also show that under heavy-tailed losses, the proposed procedure cannot simply be replaced with naive cross-validation. Taken together, we have a scalable method with transparent guarantees, which performs well without prior knowledge of how "convenient" the feedback it receives will be.