  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.
