Robust variance-regularized risk minimization with concomitant scaling

TL;DR

This paper introduces a simple, robust method for risk minimization that combines mean and standard deviation without estimating variance, performing well across various datasets.

Contribution

It proposes a novel variance-regularized risk minimization technique that is easy to implement and integrates seamlessly with standard gradient-based methods.

Findings

Performs comparably or better than CVaR and DRO-based methods

Effective on diverse datasets

Simple to incorporate into existing workflows

Abstract

Under losses which are potentially heavy-tailed, we consider the task of minimizing sums of the loss mean and standard deviation, without trying to accurately estimate the variance. By modifying a technique for variance-free robust mean estimation to fit our problem setting, we derive a simple learning procedure which can be easily combined with standard gradient-based solvers to be used in traditional machine learning workflows. Empirically, we verify that our proposed approach, despite its simplicity, performs as well or better than even the best-performing candidates derived from alternative criteria such as CVaR or DRO risks on a variety of datasets.