A unified recursion framework for stochastic variance-reduced estimation yields high-probability bounds and the first Õ(ε^{-3}) oracle complexity for stochastic optimization with expectation constraints.
Accelerated stochastic approximation with state-dependent noise.arXiv preprint arXiv:2307.01497, 2023
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Normalized momentum SGD and variance-reduced STORM achieve O(ε^{-6}) and O(ε^{-4}) oracle complexities respectively under quadratic distance-dependent noise in nonconvex stochastic optimization.
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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Unified High-Probability Analysis of Stochastic Variance-Reduced Estimation
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Normalized momentum SGD and variance-reduced STORM achieve O(ε^{-6}) and O(ε^{-4}) oracle complexities respectively under quadratic distance-dependent noise in nonconvex stochastic optimization.
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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.