Increasing mini-batch sizes in SGD under alpha-stable heavy-tailed noise yield improved L^p convergence rates, convergence in probability with constant stepsizes, and explicit stable distributional limits for the iterates and Polyak-Ruppert averages.
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Convergence of Stochastic Gradient Descent with mini-batching and infinite variance
Increasing mini-batch sizes in SGD under alpha-stable heavy-tailed noise yield improved L^p convergence rates, convergence in probability with constant stepsizes, and explicit stable distributional limits for the iterates and Polyak-Ruppert averages.