Adam's O(1/T^1/4) convergence is proven from a sign-like descent perspective, but the dimension-free claim depends on restrictive coordinate-wise assumptions.
Lower bounds for non-convex stochastic optimization.Mathematical Programming, 199(1-2):165–214, 2023
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Simple Convergence Proof of Adam From a Sign-like Descent Perspective
Adam's O(1/T^1/4) convergence is proven from a sign-like descent perspective, but the dimension-free claim depends on restrictive coordinate-wise assumptions.