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.
Parameter-free clipped gradient descent meets polyak.Advances in Neural Information Processing Systems, 37: 44575–44599, 2024
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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.