  We prove that the proximal stochastic subgradient method, applied to a weakly
convex problem, drives the gradient of the Moreau envelope to zero at the rate
$O(k^{-1/4})$. As a consequence, we resolve an open question on the convergence
rate of the proximal stochastic gradient method for minimizing the sum of a
smooth nonconvex function and a convex proximable function.
