A self-normalized subsampling method builds asymptotically valid confidence regions for Polyak–Ruppert averaged SGD under finite- or infinite-variance gradient noise.
Opti- mal variance-reduced stochastic approximation in Banach spaces.arXiv preprint arXiv:2201.08518, 2022a
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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.
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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Statistical Inference for Stochastic Gradient Descent: Beyond Finite Variance
A self-normalized subsampling method builds asymptotically valid confidence regions for Polyak–Ruppert averaged SGD under finite- or infinite-variance gradient noise.
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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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Under nested local linearity, nonlinear two-time-scale SA achieves finite-time decoupled convergence; nonlinearity in the slow update alone can destroy it.