Batched normalized SGD with momentum reaches the optimal heavy-tailed nonconvex rate without gradient clipping, and attains a slower but parameter-free rate when the tail index is unknown.
Generalized-smooth nonconvex optimization is as efficient as smooth nonconvex optimization
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Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping
Batched normalized SGD with momentum reaches the optimal heavy-tailed nonconvex rate without gradient clipping, and attains a slower but parameter-free rate when the tail index is unknown.