Technical Note-On the Convergence Rate of Stochastic Approximation for Gradient-Based Stochastic Optimization
成果类型：
Article
署名作者：
Hu, Jiaqiao; Fu, Michael C.
署名单位：
State University of New York (SUNY) System; Stony Brook University; University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.2023.0055
发表日期：
2025
关键词：
摘要：
We consider stochastic optimization via gradient -based search. Under a stochastic approximation framework, we apply a recently developed convergence rate analysis to provide a new finite -time error bound for a class of problems with convex differentiable structures. For noisy black -box functions, our main result allows us to derive finite -time bounds in the setting where the gradients are estimated via finite -difference estimators, including those based on randomized directions such as the simultaneous perturbation stochastic approximation algorithm. In particular, the convergence rate analysis sheds light on when it may be advantageous to use such randomized gradient estimates in terms of problem dimension and noise levels.
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