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.
Ro- bustness to unbounded smoothness of generalized signsgd.Advances in neural information processing systems, 35:9955–9968, 2022
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Beyond Bounded Variance: Variance-Reduced Normalized Methods for Nonconvex Optimization under Blum-Gladyshev Noise
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.