Muon with Nesterov momentum and inexact polar decomposition achieves optimal convergence rates of O(ε^(-(3α-2)/(α-1))) under heavy-tailed noise for ε-stationary points in non-convex settings.
Nesterov.Introductory Lectures on Convex Optimization: A Basic Course, volume 87 of Applied Optimization
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Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition
Muon with Nesterov momentum and inexact polar decomposition achieves optimal convergence rates of O(ε^(-(3α-2)/(α-1))) under heavy-tailed noise for ε-stationary points in non-convex settings.