New Berry-Esseen bounds for multivariate martingale difference sequences achieve n^{-1/4} rate and polylog(d) dimension dependence in Kolmogorov distance.
Online statistical inference for nonlinear stochastic approximation with Markovian data.arXiv preprint arXiv:2302.07690, 2023a
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Under nested local linearity, nonlinear two-time-scale SA achieves finite-time decoupled convergence; nonlinearity in the slow update alone can destroy it.
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Berry-Esseen bounds for multivariate martingale difference sequences in the Kolmogorov distance
New Berry-Esseen bounds for multivariate martingale difference sequences achieve n^{-1/4} rate and polylog(d) dimension dependence in Kolmogorov distance.
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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.