Establishes Omega(epsilon^{-6}) and Omega(epsilon^{-4}) lower bounds under BG-0 variance for smooth and mean-square smooth non-convex optimization and presents PASTA achieving matching minimax rates.
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Lower Bounds and Proximally Anchored SGD for Non-Convex Minimization Under Unbounded Variance
Establishes Omega(epsilon^{-6}) and Omega(epsilon^{-4}) lower bounds under BG-0 variance for smooth and mean-square smooth non-convex optimization and presents PASTA achieving matching minimax rates.