  In deep learning, different kinds of deep networks typically need different
optimizers, which have to be chosen after multiple trials, making the training
process inefficient. To relieve this issue and consistently improve the model
training speed across deep networks, we propose the ADAptive Nesterov momentum
algorithm, Adan for short. Adan first reformulates the vanilla Nesterov
acceleration to develop a new Nesterov momentum estimation (NME) method, which
avoids the extra overhead of computing gradient at the extrapolation point.
Then Adan adopts NME to estimate the gradient's first- and second-order moments
in adaptive gradient algorithms for convergence acceleration. Besides, we prove
that Adan finds an $\epsilon$-approximate first-order stationary point within
$O(\epsilon^{-3.5})$ stochastic gradient complexity on the non-convex
stochastic problems (e.g., deep learning problems), matching the best-known
lower bound. Extensive experimental results show that Adan consistently
surpasses the corresponding SoTA optimizers on vision, language, and RL tasks
and sets new SoTAs for many popular networks and frameworks, e.g., ResNet,
ConvNext, ViT, Swin, MAE, DETR, GPT-2, Transformer-XL, and BERT. More
surprisingly, Adan can use half of the training cost (epochs) of SoTA
optimizers to achieve higher or comparable performance on ViT, GPT-2, MAE,
e.t.c., and also shows great tolerance to a large range of minibatch size,
e.g., from 1k to 32k. Code is released at https://github.com/sail-sg/Adan, and
has been used in multiple popular deep learning frameworks or projects.
