First Order Methods with Markovian Noise: from Acceleration to Variational Inequalities

arXiv:2305.15938v2 Announce Type: replace-cross
Abstract: This paper delves into stochastic optimization problems that involve Markovian noise. We present a unified approach for the theoretical analysis of first-order gradient methods for stochastic optimization and variational inequalities. Our approach covers scenarios for both non-convex and strongly convex minimization problems. To achieve an optimal (linear) dependence on the mixing time of the underlying noise sequence, we use the randomized batching scheme, which is based on the multilevel Monte Carlo method. Moreover, our technique …

abstract analysis arxiv cs.lg gradient math.oc noise optimization paper stat.ml stochastic type