We study the idea of variance reduction applied to adaptive stochastic mirror
descent algorithms in nonsmooth nonconvex finite-sum optimization problems. We
propose a simple yet generalized adaptive mirror descent algorithm with
variance reduction named SVRAMD and provide its convergence analysis in
different settings. We prove that variance reduction reduces the gradient
complexity of most adaptive mirror descent algorithms and boost their
convergence. In particular, our general theory implies variance reduction can
be applied to algorithms using time-varying step sizes and self-adaptive
algorithms such as AdaGrad and RMSProp. Moreover, our convergence rates recover
the best existing rates of non-adaptive algorithms. We check the validity of
our claims using experiments in deep learning.Comment: NeurIPS 2020 OPT worksho