A Generalized Version of Chung’s Lemma and its Applications
arXiv:2406.05637v2 Announce Type: replace-cross Abstract: Chung’s Lemma is a classical tool for establishing asymptotic convergence rates of (stochastic) optimization methods under strong convexity-type assumptions and appropriate polynomial diminishing step sizes. In this work, we develop a generalized version of Chung’s Lemma, which provides a simple non-asymptotic convergence framework for a more general family of step size rules. We demonstrate broad applicability of the proposed generalized lemma by deriving tight non-asymptotic convergence rates for a large variety of stochastic […]