A Rate Transfer Method: Convergence Rates in Stochastic Gradient Descent via Stochastic Calculus

Abstract:We develop a rate-transfer method that converts finite-time Lyapunov estimates for an associated stochastic differential equation (SDE) into finite-time convergence bounds for stochastic gradient algorithms. Under generic moment and smoothness conditions, the convergence analysis of the stochastic gradient method reduces to a calculus argument verifying a Lyapunov generator inequality for the SDE. The method recovers established rates for classical stochastic gradient methods and provides a way to establish convergence rates for new optimization algorithms through calculus arguments applied to their associated SDEs.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Optimization and Control (math.OC); Probability (math.PR); Machine Learning (stat.ML)

G.1.6; G.3; I.2.6

arXiv:2610.18739 [cs.LG]

(or arXiv:2610.18739v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.18739 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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