Title: Win: Weight-Decay-Integrated Nesterov Acceleration for Adaptive Gradient Algorithms. Abstract: Training deep  networks on  large-scale datasets is computationally challenging.  In this work, we explore the problem of ``\textit{how to  accelerate  adaptive gradient algorithms in a general manner}", and aim to provide practical efficiency-boosting insights.   To this end, we   propose an effective and general   {Weight-decay-Integrated Nesterov acceleration} (Win) to accelerate adaptive  algorithms. Taking AdamW and Adam as examples,  we minimize a dynamical   loss per iteration which combines the vanilla training loss and a dynamic regularizer inspired by proximal point method (PPM) to improve the convexity of the problem. To introduce Nesterov-alike-acceleration into AdamW and Adam,  we respectively  use the  first- and second-order Taylor approximations of vanilla loss  to  update the variable  twice. In this way,  we arrive at  our Win acceleration  for AdamW and Adam that uses  a conservative step  and a  reckless step to update twice and then linearly combines these two updates for acceleration. Next,  we  extend  Win acceleration to LAMB and SGD. Our transparent acceleration derivation  could  provide insights for  other accelerated methods and their integration into  adaptive algorithms.  Besides, we prove the convergence of Win-accelerated adaptive  algorithms and  justify their convergence superiority over their non-accelerated counterparts by taking AdamW and Adam as examples.  Experimental results testify to the faster convergence speed and superior performance of our Win-accelerated AdamW, Adam, LAMB and SGD over their non-accelerated counterparts on vision classification tasks and  language modeling tasks with both CNN and Transformer backbones.  We hope Win  shall be a default acceleration option for  popular optimizers in deep learning community to improve the training efficiency. Code will be released at \url{https://github.com/sail-sg/win}.