Year: 2025
Type: article
Abstract: We analyze the convergence rates of stochastic approximation algorithms under nonvanishing gradient conditions. For these sharp (V-shaped) functions, standard Gaussian approximations fail, making tighter exponential concentration bounds more suitable. We prove that stochastic approximation algorithms, including Projected Stochastic Gradient Descent (PSGD), Kiefer-Wolfowitz, and Frank-Wolfe algorithms, exhibit exponential concentration near an optimum. A consequence is faster convergence rates, notably linear convergence, and O(1/t) rates. The paper leverages techniques from Markov chain theory, specifically geometric ergodicity and Lyapunov drift analysis, thereby extending previous results by Hajek (1982) .
Source: Operations Research
Authors: Kody J. H. Law, Neil Walton, Shangda Yang
Institutions: University of Manchester, Durham University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409654251