Robust variance-regularized risk minimization with concomitant scaling
This addresses robust risk minimization for machine learning applications where data may have heavy-tailed distributions, though it appears incremental as it modifies an existing technique for a specific setting.
The paper tackles the problem of minimizing sums of loss mean and standard deviation under potentially heavy-tailed losses, without needing accurate variance estimation, and shows that their simple gradient-based method performs as well or better than alternatives like CVaR or DRO on various datasets.
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.