  In a recent paper, we showed that the stochastic subgradient method applied
to a weakly convex problem, drives the gradient of the Moreau envelope to zero
at the rate $O(k^{-1/4})$. In this supplementary note, we present a stochastic
subgradient method for minimizing a convex function, with the improved rate
$\widetilde O(k^{-1/2})$.
