tldr: This paper stabilizes Nesterov's lookahead acceleration for deep learning by replacing the classical lookahead direction with an exponential moving averaged lookahead. The resulting EMA-Nesterov method preserves accelerated convergence guarantees in convex settings and accelerates many common optimization algorithms, e.g., Muon, SOAP, Adam, in language model pre-training.
EMA-Nesterov move towards a stable lookahead direction (green).
EMA-Nesterov accelerates Muon by 6% in NanoGPT Track 3 speed run.