AdaGrad-type algorithms provably need a complexity quadratic in the initial gap and smoothness constants under relaxed smoothness, so they cannot match the optimal rate of clipped SGD.
Let algorithmADAN denote Decorrelated AdaGrad-Norm with parameters η >0 and 0<γ ≤ ∆ L1 8 log ( 1 + 48 ∆ L2 1 L0 )
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Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness
AdaGrad-type algorithms provably need a complexity quadratic in the initial gap and smoothness constants under relaxed smoothness, so they cannot match the optimal rate of clipped SGD.