SignSGD with momentum attains O(d^{1/2}T^{-1/4}) gradient-norm convergence under standard L2 smoothness and O(T^{-1/4}) under L-infinity smoothness, with improved distributed majority-vote rates.
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Improved Analysis for Sign-based Methods with Momentum Updates
SignSGD with momentum attains O(d^{1/2}T^{-1/4}) gradient-norm convergence under standard L2 smoothness and O(T^{-1/4}) under L-infinity smoothness, with improved distributed majority-vote rates.