Bunch of optimizer implementations in PyTorch with clean-code, strict types. Also, including useful optimization ideas.
Most of the implementations are based on the original paper, but I added some tweaks.
Highly inspired by pytorch-optimizer.




$ pip3 install pytorch-optimizer

Simple Usage

from pytorch_optimizer import Ranger21

model = YourModel()
optimizer = Ranger21(model.parameters())

for input, output in data:
  loss = loss_function(output, model(input))

Supported Optimizers

Optimizer Description Official Code Paper
AdaBelief Adapting Stepsizes by the Belief in Observed Gradients github
AdaBound Adaptive Gradient Methods with Dynamic Bound of Learning Rate github
AdaHessian An Adaptive Second Order Optimizer for Machine Learning github
AdamP Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights github
diffGrad An Optimization Method for Convolutional Neural Networks github
MADGRAD A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic github
RAdam On the Variance of the Adaptive Learning Rate and Beyond github
Ranger a synergistic optimizer combining RAdam and LookAhead, and now GC in one optimizer github
Ranger21 a synergistic deep learning optimizer github

Useful Resources

Several optimization ideas to regularize & stabilize the training. Most of the ideas are applied in Ranger21 optimizer.

Also, most of the captures are taken from Ranger21 paper.

Adaptive Gradient Clipping Gradient Centralization Softplus Transformation
Gradient Normalization Norm Loss Positive-Negative Momentum
Linear learning rate warmup Stable weight decay Explore-exploit learning rate schedule
Lookahead Chebyshev learning rate schedule (Adaptive) Sharpness-Aware Minimization
On the Convergence of Adam and Beyond    

Adaptive Gradient Clipping

This idea originally proposed in NFNet (Normalized-Free Network) paper.
AGC (Adaptive Gradient Clipping) clips gradients based on the unit-wise ratio of gradient norms to parameter norms.

Gradient Centralization

Gradient Centralization (GC) operates directly on gradients by centralizing the gradient to have zero mean.

Softplus Transformation

By running the final variance denom through the softplus function, it lifts extremely tiny values to keep them viable.

Gradient Normalization

Norm Loss

Positive-Negative Momentum

Linear learning rate warmup

Stable weight decay

Explore-exploit learning rate schedule


k steps forward, 1 step back. Lookahead consisting of keeping an exponential moving average of the weights that is
updated and substituted to the current weights every k_{lookahead} steps (5 by default).

Chebyshev learning rate schedule

Acceleration via Fractal Learning Rate Schedules

(Adaptive) Sharpness-Aware Minimization

Sharpness-Aware Minimization (SAM) simultaneously minimizes loss value and loss sharpness.
In particular, it seeks parameters that lie in neighborhoods having uniformly low loss.

On the Convergence of Adam and Beyond



    title={AdamP: Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights},
    author={Heo, Byeongho and Chun, Sanghyuk and Oh, Seong Joon and Han, Dongyoon and Yun, Sangdoo and Kim, Gyuwan and Uh, Youngjung and Ha, Jung-Woo},
    booktitle={International Conference on Learning Representations (ICLR)},

Adaptive Gradient Clipping (AGC)

  author={Andrew Brock and Soham De and Samuel L. Smith and Karen Simonyan},
  title={High-Performance Large-Scale Image Recognition Without Normalization},
  journal={arXiv preprint arXiv:2102.06171},

Chebyshev LR Schedules

  title={Acceleration via Fractal Learning Rate Schedules},
  author={Agarwal, Naman and Goel, Surbhi and Zhang, Cyril},
  journal={arXiv preprint arXiv:2103.01338},

Gradient Centralization (GC)

  title={Gradient centralization: A new optimization technique for deep neural networks},
  author={Yong, Hongwei and Huang, Jianqiang and Hua, Xiansheng and Zhang, Lei},
  booktitle={European Conference on Computer Vision},


  title={Lookahead optimizer: k steps forward, 1 step back},
  author={Zhang, Michael R and Lucas, James and Hinton, Geoffrey and Ba, Jimmy},
  journal={arXiv preprint arXiv:1907.08610},


 author = {Liu, Liyuan and Jiang, Haoming and He, Pengcheng and Chen, Weizhu and Liu, Xiaodong and Gao, Jianfeng and Han, Jiawei},
 booktitle = {Proceedings of the Eighth International Conference on Learning Representations (ICLR 2020)},
 month = {April},
 title = {On the Variance of the Adaptive Learning Rate and Beyond},
 year = {2020}

Norm Loss

  title={Norm Loss: An efficient yet effective regularization method for deep neural networks},
  author={Georgiou, Theodoros and Schmitt, Sebastian and B{\"a}ck, Thomas and Chen, Wei and Lew, Michael},
  booktitle={2020 25th International Conference on Pattern Recognition (ICPR)},

Positive-Negative Momentum

  title={Positive-Negative Momentum: Manipulating Stochastic Gradient Noise to Improve Generalization},
  author={Xie, Zeke and Yuan, Li and Zhu, Zhanxing and Sugiyama, Masashi},
  journal={arXiv preprint arXiv:2103.17182},

Explore-Exploit learning rate schedule

  title={Wide-minima Density Hypothesis and the Explore-Exploit Learning Rate Schedule},
  author={Iyer, Nikhil and Thejas, V and Kwatra, Nipun and Ramjee, Ramachandran and Sivathanu, Muthian},
  journal={arXiv preprint arXiv:2003.03977},

Linear learning-rate warm-up

  title={On the adequacy of untuned warmup for adaptive optimization},
  author={Ma, Jerry and Yarats, Denis},
  journal={arXiv preprint arXiv:1910.04209},

Stable weight decay

  title={Stable weight decay regularization},
  author={Xie, Zeke and Sato, Issei and Sugiyama, Masashi},
  journal={arXiv preprint arXiv:2011.11152},

Softplus transformation

  title={Calibrating the adaptive learning rate to improve convergence of adam},
  author={Tong, Qianqian and Liang, Guannan and Bi, Jinbo},
  journal={arXiv preprint arXiv:1908.00700},


  title={Adaptivity without compromise: a momentumized, adaptive, dual averaged gradient method for stochastic optimization},
  author={Defazio, Aaron and Jelassi, Samy},
  journal={arXiv preprint arXiv:2101.11075},


  title={ADAHESSIAN: An adaptive second order optimizer for machine learning},
  author={Yao, Zhewei and Gholami, Amir and Shen, Sheng and Mustafa, Mustafa and Keutzer, Kurt and Mahoney, Michael W},
  journal={arXiv preprint arXiv:2006.00719},


  author = {Luo, Liangchen and Xiong, Yuanhao and Liu, Yan and Sun, Xu},
  title = {Adaptive Gradient Methods with Dynamic Bound of Learning Rate},
  booktitle = {Proceedings of the 7th International Conference on Learning Representations},
  month = {May},
  year = {2019},
  address = {New Orleans, Louisiana}


  title={Adabelief optimizer: Adapting stepsizes by the belief in observed gradients},
  author={Zhuang, Juntang and Tang, Tommy and Ding, Yifan and Tatikonda, Sekhar and Dvornek, Nicha and Papademetris, Xenophon and Duncan, James S},
  journal={arXiv preprint arXiv:2010.07468},

Sharpness-Aware Minimization

  title={Sharpness-aware minimization for efficiently improving generalization},
  author={Foret, Pierre and Kleiner, Ariel and Mobahi, Hossein and Neyshabur, Behnam},
  journal={arXiv preprint arXiv:2010.01412},

Adaptive Sharpness-Aware Minimization

  title={ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks},
  author={Kwon, Jungmin and Kim, Jeongseop and Park, Hyunseo and Choi, In Kwon},
  journal={arXiv preprint arXiv:2102.11600},


  title={diffgrad: An optimization method for convolutional neural networks},
  author={Dubey, Shiv Ram and Chakraborty, Soumendu and Roy, Swalpa Kumar and Mukherjee, Snehasis and Singh, Satish Kumar and Chaudhuri, Bidyut Baran},
  journal={IEEE transactions on neural networks and learning systems},

On the Convergence of Adam and Beyond

  title={On the convergence of adam and beyond},
  author={Reddi, Sashank J and Kale, Satyen and Kumar, Sanjiv},
  journal={arXiv preprint arXiv:1904.09237},


Hyeongchan Kim / @kozistr