  In this work, we study a new class of risks defined in terms of the location
and deviation of the loss distribution, generalizing far beyond classical
mean-variance risk functions. The class is easily implemented as a wrapper
around any smooth loss, it admits finite-sample stationarity guarantees for
stochastic gradient methods, it is straightforward to interpret and adjust,
with close links to M-estimators of the loss location, and has a salient effect
on the test loss distribution.
