  We investigate the stochastic optimization problem of minimizing population
risk, where the loss defining the risk is assumed to be weakly convex.
Compositions of Lipschitz convex functions with smooth maps are the primary
examples of such losses. We analyze the estimation quality of such nonsmooth
and nonconvex problems by their sample average approximations. Our main results
establish dimension-dependent rates on subgradient estimation in full
generality and dimension-independent rates when the loss is a generalized
linear model. As an application of the developed techniques, we analyze the
nonsmooth landscape of a robust nonlinear regression problem.
