Learning with risks based on M-location

Abstract In this work, we study a new class of risks defined in terms the location and deviation loss distribution, generalizing far beyond classical mean-variance risk functions. The is easily implemented as wrapper around any smooth loss, it admits finite-sample stationarity guarantees for stochastic gradient methods, straightforward to interpret adjust, with close links M-estimators location, has salient effect on test giving us control over symmetry deviations that are not possible under naive ERM.