Under nested local linearity, nonlinear two-time-scale SA achieves finite-time decoupled convergence; nonlinearity in the slow update alone can destroy it.
Fast nonlinear two-time-scale stochastic approximation: AchievingO(1/k) finite- sample complexity.arXiv preprint arXiv:2401.12764,
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Finite-Time Decoupled Convergence in Nonlinear Two-Time-Scale Stochastic Approximation
Under nested local linearity, nonlinear two-time-scale SA achieves finite-time decoupled convergence; nonlinearity in the slow update alone can destroy it.