Taming Nonconvex Stochastic Mirror Descent with General Bregman Divergence

arXiv:2402.17722v1 Announce Type: cross
Abstract: This paper revisits the convergence of Stochastic Mirror Descent (SMD) in the contemporary nonconvex optimization setting. Existing results for batch-free nonconvex SMD restrict the choice of the distance generating function (DGF) to be differentiable with Lipschitz continuous gradients, thereby excluding important setups such as Shannon entropy. In this work, we present a new convergence analysis of nonconvex SMD supporting general DGF, that overcomes the above limitations and relies solely on the standard assumptions. Moreover, our …

abstract arxiv continuous convergence cs.lg differentiable divergence entropy free function general math.oc optimization paper results stochastic type