Establishes maximal concentration bounds for stochastic approximation under heavy-tailed Markovian noise, with tails ranging from sub-Gaussian to heavier than Weibull depending on step sizes and contractivity properties, plus a truncation argument for unbounded noise.
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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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Concentration of General Stochastic Approximation Under Heavy-Tailed Markovian Noise
Establishes maximal concentration bounds for stochastic approximation under heavy-tailed Markovian noise, with tails ranging from sub-Gaussian to heavier than Weibull depending on step sizes and contractivity properties, plus a truncation argument for unbounded noise.
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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.