Muon-MVR2 attains the optimal anytime convergence rate of ~O(T^{-1/3}) in stochastic non-convex settings under horizon-free schedules.
Convergence of adam for non-convex objectives: Relaxed hyperparameters and non-ergodic case
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OptMuon combines orthogonalized momentum with trajectory-dependent AdaGrad-Norm adaptation to obtain expected-stationarity rates of order T^{-1/2} + sigma^{1/2}T^{-1/4} or T^{-1/2} + sigma^{1/3}T^{-1/3} that reduce to near-optimal deterministic first-order rates in the zero-noise regime.
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On the Convergence of Muon and Beyond
Muon-MVR2 attains the optimal anytime convergence rate of ~O(T^{-1/3}) in stochastic non-convex settings under horizon-free schedules.
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OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality
OptMuon combines orthogonalized momentum with trajectory-dependent AdaGrad-Norm adaptation to obtain expected-stationarity rates of order T^{-1/2} + sigma^{1/2}T^{-1/4} or T^{-1/2} + sigma^{1/3}T^{-1/3} that reduce to near-optimal deterministic first-order rates in the zero-noise regime.