  In this paper, we investigate the non-asymptotic stationary convergence
behavior of Stochastic Mirror Descent (SMD) for nonconvex optimization. We
focus on a general class of nonconvex nonsmooth stochastic optimization
problems, in which the objective can be decomposed into a relatively weakly
convex function (possibly non-Lipschitz) and a simple non-smooth convex
regularizer. We prove that SMD, without the use of mini-batch, is guaranteed to
converge to a stationary point in a convergence rate of $
\mathcal{O}(1/\sqrt{t}) $. The efficiency estimate matches with existing
results for stochastic subgradient method, but is evaluated under a stronger
stationarity measure. Our convergence analysis applies to both the original SMD
and its proximal version, as well as the deterministic variants, for solving
relatively weakly convex problems.
