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Fast Nonlinear Two-Time-Scale Stochastic Approximation: Achieving $O(1/k)$ Finite-Sample Complexity
March 25, 2024, 4:43 a.m. | Thinh T. Doan
cs.LG updates on arXiv.org arxiv.org
Abstract: This paper proposes to develop a new variant of the two-time-scale stochastic approximation to find the roots of two coupled nonlinear operators, assuming only noisy samples of these operators can be observed. Our key idea is to leverage the classic Ruppert-Polyak averaging technique to dynamically estimate the operators through their samples. The estimated values of these averaging steps will then be used in the two-time-scale stochastic approximation updates to find the desired solution. Our main …
abstract approximation arxiv complexity cs.lg key math.oc operators paper sample samples scale stochastic type
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