pytorch-optimizer

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The reasons why you use pytorch-optimizer.

• Wide range of supported optimizers. Currently, 106 optimizers (+ bitsandbytes, qgalore, torchao), 16 lr schedulers, and 13 loss functions are supported!
• Including many variants such as ADOPT, Cautious, AdamD, StableAdamW, and Gradient Centrailiaztion
• Easy to use, clean, and tested codes
• Active maintenance
• Somewhat a bit more optimized compared to the original implementation

Highly inspired by pytorch-optimizer.

Getting Started

For more, see the documentation.

Most optimizers are under MIT or Apache 2.0 license, but a few optimizers like Fromage, Nero have CC BY-NC-SA 4.0 license, which is non-commercial. So, please double-check the license before using it at your work.

Installation

$ pip3 install pytorch-optimizer

From v2.12.0, v3.1.0, you can use bitsandbytes, q-galore-torch, torchao optimizers respectively! please check the bnb requirements, q-galore-torch installation, torchao installation before installing it.

From v3.0.0, drop Python 3.7 support. However, you can still use this package with Python 3.7 by installing with --ignore-requires-python option.

Simple Usage

from pytorch_optimizer import AdamP

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

# or you can use optimizer loader, simply passing a name of the optimizer.

from pytorch_optimizer import load_optimizer

optimizer = load_optimizer(optimizer='adamp')(model.parameters())

# if you install `bitsandbytes` optimizer, you can use `8-bit` optimizers from `pytorch-optimizer`.

optimizer = load_optimizer(optimizer='bnb_adamw8bit')(model.parameters())

Also, you can load the optimizer via torch.hub.

import torch

model = YourModel()

opt = torch.hub.load('kozistr/pytorch_optimizer', 'adamp')
optimizer = opt(model.parameters())

If you want to build the optimizer with parameters & configs, there's create_optimizer() API.

from pytorch_optimizer import create_optimizer

optimizer = create_optimizer(
    model,
    'adamp',
    lr=1e-3,
    weight_decay=1e-3,
    use_gc=True,
    use_lookahead=True,
    use_orthograd=False,
)

Supported Optimizers

You can check the supported optimizers with below code.

from pytorch_optimizer import get_supported_optimizers

supported_optimizers = get_supported_optimizers()

or you can also search them with the filter(s).

from pytorch_optimizer import get_supported_optimizers

get_supported_optimizers('adam*')
# ['adamax', 'adamg', 'adammini', 'adamod', 'adamp', 'adams', 'adamw']

get_supported_optimizers(['adam*', 'ranger*'])
# ['adamax', 'adamg', 'adammini', 'adamod', 'adamp', 'adams', 'adamw', 'ranger', 'ranger21']

Optimizer	Description	Official Code	Paper	Citation
AdaBelief	Adapting Step-sizes by the Belief in Observed Gradients	github	https://arxiv.org/abs/2010.07468	cite
AdaBound	Adaptive Gradient Methods with Dynamic Bound of Learning Rate	github	https://openreview.net/forum?id=Bkg3g2R9FX	cite
AdaHessian	An Adaptive Second Order Optimizer for Machine Learning	github	https://arxiv.org/abs/2006.00719	cite
AdamD	Improved bias-correction in Adam		https://arxiv.org/abs/2110.10828	cite
AdamP	Slowing Down the Slowdown for Momentum Optimizers on Scale-invariant Weights	github	https://arxiv.org/abs/2006.08217	cite
diffGrad	An Optimization Method for Convolutional Neural Networks	github	https://arxiv.org/abs/1909.11015v3	cite
MADGRAD	A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic	github	https://arxiv.org/abs/2101.11075	cite
RAdam	On the Variance of the Adaptive Learning Rate and Beyond	github	https://arxiv.org/abs/1908.03265	cite
Ranger	a synergistic optimizer combining RAdam and LookAhead, and now GC in one optimizer	github	https://bit.ly/3zyspC3	cite
Ranger21	a synergistic deep learning optimizer	github	https://arxiv.org/abs/2106.13731	cite
Lamb	Large Batch Optimization for Deep Learning	github	https://arxiv.org/abs/1904.00962	cite
Shampoo	Preconditioned Stochastic Tensor Optimization	github	https://arxiv.org/abs/1802.09568	cite
Nero	Learning by Turning: Neural Architecture Aware Optimisation	github	https://arxiv.org/abs/2102.07227	cite
Adan	Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models	github	https://arxiv.org/abs/2208.06677	cite
Adai	Disentangling the Effects of Adaptive Learning Rate and Momentum	github	https://arxiv.org/abs/2006.15815	cite
SAM	Sharpness-Aware Minimization	github	https://arxiv.org/abs/2010.01412	cite
ASAM	Adaptive Sharpness-Aware Minimization	github	https://arxiv.org/abs/2102.11600	cite
GSAM	Surrogate Gap Guided Sharpness-Aware Minimization	github	https://openreview.net/pdf?id=edONMAnhLu-	cite
D-Adaptation	Learning-Rate-Free Learning by D-Adaptation	github	https://arxiv.org/abs/2301.07733	cite
AdaFactor	Adaptive Learning Rates with Sublinear Memory Cost	github	https://arxiv.org/abs/1804.04235	cite
Apollo	An Adaptive Parameter-wise Diagonal Quasi-Newton Method for Nonconvex Stochastic Optimization	github	https://arxiv.org/abs/2009.13586	cite
NovoGrad	Stochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks	github	https://arxiv.org/abs/1905.11286	cite
Lion	Symbolic Discovery of Optimization Algorithms	github	https://arxiv.org/abs/2302.06675	cite
Ali-G	Adaptive Learning Rates for Interpolation with Gradients	github	https://arxiv.org/abs/1906.05661	cite
SM3	Memory-Efficient Adaptive Optimization	github	https://arxiv.org/abs/1901.11150	cite
AdaNorm	Adaptive Gradient Norm Correction based Optimizer for CNNs	github	https://arxiv.org/abs/2210.06364	cite
RotoGrad	Gradient Homogenization in Multitask Learning	github	https://openreview.net/pdf?id=T8wHz4rnuGL	cite
A2Grad	Optimal Adaptive and Accelerated Stochastic Gradient Descent	github	https://arxiv.org/abs/1810.00553	cite
AccSGD	Accelerating Stochastic Gradient Descent For Least Squares Regression	github	https://arxiv.org/abs/1704.08227	cite
SGDW	Decoupled Weight Decay Regularization	github	https://arxiv.org/abs/1711.05101	cite
ASGD	Adaptive Gradient Descent without Descent	github	https://arxiv.org/abs/1910.09529	cite
Yogi	Adaptive Methods for Nonconvex Optimization		NIPS 2018	cite
SWATS	Improving Generalization Performance by Switching from Adam to SGD		https://arxiv.org/abs/1712.07628	cite
Fromage	On the distance between two neural networks and the stability of learning	github	https://arxiv.org/abs/2002.03432	cite
MSVAG	Dissecting Adam: The Sign, Magnitude and Variance of Stochastic Gradients	github	https://arxiv.org/abs/1705.07774	cite
AdaMod	An Adaptive and Momental Bound Method for Stochastic Learning	github	https://arxiv.org/abs/1910.12249	cite
AggMo	Aggregated Momentum: Stability Through Passive Damping	github	https://arxiv.org/abs/1804.00325	cite
QHAdam	Quasi-hyperbolic momentum and Adam for deep learning	github	https://arxiv.org/abs/1810.06801	cite
PID	A PID Controller Approach for Stochastic Optimization of Deep Networks	github	CVPR 18	cite
Gravity	a Kinematic Approach on Optimization in Deep Learning	github	https://arxiv.org/abs/2101.09192	cite
AdaSmooth	An Adaptive Learning Rate Method based on Effective Ratio		https://arxiv.org/abs/2204.00825v1	cite
SRMM	Stochastic regularized majorization-minimization with weakly convex and multi-convex surrogates	github	https://arxiv.org/abs/2201.01652	cite
AvaGrad	Domain-independent Dominance of Adaptive Methods	github	https://arxiv.org/abs/1912.01823	cite
PCGrad	Gradient Surgery for Multi-Task Learning	github	https://arxiv.org/abs/2001.06782	cite
AMSGrad	On the Convergence of Adam and Beyond		https://openreview.net/pdf?id=ryQu7f-RZ	cite
Lookahead	k steps forward, 1 step back	github	https://arxiv.org/abs/1907.08610	cite
PNM	Manipulating Stochastic Gradient Noise to Improve Generalization	github	https://arxiv.org/abs/2103.17182	cite
GC	Gradient Centralization	github	https://arxiv.org/abs/2004.01461	cite
AGC	Adaptive Gradient Clipping	github	https://arxiv.org/abs/2102.06171	cite
Stable WD	Understanding and Scheduling Weight Decay	github	https://arxiv.org/abs/2011.11152	cite
Softplus T	Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM		https://arxiv.org/abs/1908.00700	cite
Un-tuned w/u	On the adequacy of untuned warmup for adaptive optimization		https://arxiv.org/abs/1910.04209	cite
Norm Loss	An efficient yet effective regularization method for deep neural networks		https://arxiv.org/abs/2103.06583	cite
AdaShift	Decorrelation and Convergence of Adaptive Learning Rate Methods	github	https://arxiv.org/abs/1810.00143v4	cite
AdaDelta	An Adaptive Learning Rate Method		https://arxiv.org/abs/1212.5701v1	cite
Amos	An Adam-style Optimizer with Adaptive Weight Decay towards Model-Oriented Scale	github	https://arxiv.org/abs/2210.11693	cite
SignSGD	Compressed Optimisation for Non-Convex Problems	github	https://arxiv.org/abs/1802.04434	cite
Sophia	A Scalable Stochastic Second-order Optimizer for Language Model Pre-training	github	https://arxiv.org/abs/2305.14342	cite
Prodigy	An Expeditiously Adaptive Parameter-Free Learner	github	https://arxiv.org/abs/2306.06101	cite
PAdam	Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks	github	https://arxiv.org/abs/1806.06763	cite
LOMO	Full Parameter Fine-tuning for Large Language Models with Limited Resources	github	https://arxiv.org/abs/2306.09782	cite
AdaLOMO	Low-memory Optimization with Adaptive Learning Rate	github	https://arxiv.org/abs/2310.10195	cite
Tiger	A Tight-fisted Optimizer, an optimizer that is extremely budget-conscious	github		cite
CAME	Confidence-guided Adaptive Memory Efficient Optimization	github	https://aclanthology.org/2023.acl-long.243/	cite
WSAM	Sharpness-Aware Minimization Revisited: Weighted Sharpness as a Regularization Term	github	https://arxiv.org/abs/2305.15817	cite
Aida	A DNN Optimizer that Improves over AdaBelief by Suppression of the Adaptive Stepsize Range	github	https://arxiv.org/abs/2203.13273	cite
GaLore	Memory-Efficient LLM Training by Gradient Low-Rank Projection	github	https://arxiv.org/abs/2403.03507	cite
Adalite	Adalite optimizer	github	https://github.com/VatsaDev/adalite	cite
bSAM	SAM as an Optimal Relaxation of Bayes	github	https://arxiv.org/abs/2210.01620	cite
Schedule-Free	Schedule-Free Optimizers	github	https://github.com/facebookresearch/schedule_free	cite
FAdam	Adam is a natural gradient optimizer using diagonal empirical Fisher information	github	https://arxiv.org/abs/2405.12807	cite
Grokfast	Accelerated Grokking by Amplifying Slow Gradients	github	https://arxiv.org/abs/2405.20233	cite
Kate	Remove that Square Root: A New Efficient Scale-Invariant Version of AdaGrad	github	https://arxiv.org/abs/2403.02648	cite
StableAdamW	Stable and low-precision training for large-scale vision-language models		https://arxiv.org/abs/2304.13013	cite
AdamMini	Use Fewer Learning Rates To Gain More	github	https://arxiv.org/abs/2406.16793	cite
TRAC	Adaptive Parameter-free Optimization	github	https://arxiv.org/abs/2405.16642	cite
AdamG	Towards Stability of Parameter-free Optimization		https://arxiv.org/abs/2405.04376	cite
AdEMAMix	Better, Faster, Older	github	https://arxiv.org/abs/2409.03137	cite
SOAP	Improving and Stabilizing Shampoo using Adam	github	https://arxiv.org/abs/2409.11321	cite
ADOPT	Modified Adam Can Converge with Any β2 with the Optimal Rate	github	https://arxiv.org/abs/2411.02853	cite
FTRL	Follow The Regularized Leader		https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/41159.pdf
Cautious	Improving Training with One Line of Code	github	https://arxiv.org/pdf/2411.16085v1	cite
DeMo	Decoupled Momentum Optimization	github	https://arxiv.org/abs/2411.19870	cite
MicroAdam	Accurate Adaptive Optimization with Low Space Overhead and Provable Convergence	github	https://arxiv.org/abs/2405.15593	cite
Muon	MomentUm Orthogonalized by Newton-schulz	github	https://x.com/kellerjordan0/status/1842300916864844014	cite
LaProp	Separating Momentum and Adaptivity in Adam	github	https://arxiv.org/abs/2002.04839	cite
APOLLO	SGD-like Memory, AdamW-level Performance	github	https://arxiv.org/abs/2412.05270	cite
MARS	Unleashing the Power of Variance Reduction for Training Large Models	github	https://arxiv.org/abs/2411.10438	cite
SGDSaI	No More Adam: Learning Rate Scaling at Initialization is All You Need	github	https://arxiv.org/abs/2411.10438	cite
Grams	Gradient Descent with Adaptive Momentum Scaling		https://arxiv.org/abs/2412.17107	cite
OrthoGrad	Grokking at the Edge of Numerical Stability	github	https://arxiv.org/abs/2501.04697	cite
Adam-ATAN2	Scaling Exponents Across Parameterizations and Optimizers		https://arxiv.org/abs/2407.05872	cite
SPAM	Spike-Aware Adam with Momentum Reset for Stable LLM Training	github	https://arxiv.org/abs/2501.06842	cite
TAM	Torque-Aware Momentum		https://arxiv.org/abs/2412.18790	cite
FOCUS	First Order Concentrated Updating Scheme	github	https://arxiv.org/abs/2501.12243	cite
PSGD	Preconditioned Stochastic Gradient Descent	github	https://arxiv.org/abs/1512.04202	cite
EXAdam	The Power of Adaptive Cross-Moments	github	https://arxiv.org/abs/2412.20302	cite
GCSAM	Gradient Centralized Sharpness Aware Minimization	github	https://arxiv.org/abs/2501.11584	cite
LookSAM	Towards Efficient and Scalable Sharpness-Aware Minimization	github	https://arxiv.org/abs/2203.02714	cite
SCION	Training Deep Learning Models with Norm-Constrained LMOs	github	https://arxiv.org/abs/2502.07529	cite
COSMOS	SOAP with Muon	github
StableSPAM	How to Train in 4-Bit More Stably than 16-Bit Adam	github	https://arxiv.org/abs/2502.17055
AdaGC	Improving Training Stability for Large Language Model Pretraining		https://arxiv.org/abs/2502.11034	cite
Simplified-Ademamix	Connections between Schedule-Free Optimizers, AdEMAMix, and Accelerated SGD Variants	github	https://arxiv.org/abs/2502.02431	cite
Fira	Can We Achieve Full-rank Training of LLMs Under Low-rank Constraint?	github	https://arxiv.org/abs/2410.01623	cite
RACS & Alice	Towards Efficient Optimizer Design for LLM via Structured Fisher Approximation with a Low-Rank Extension		https://arxiv.org/pdf/2502.07752	cite
VSGD	Variational Stochastic Gradient Descent for Deep Neural Networks	github	https://openreview.net/forum?id=xu4ATNjcdy	cite

Supported LR Scheduler

You can check the supported learning rate schedulers with below code.

from pytorch_optimizer import get_supported_lr_schedulers

supported_lr_schedulers = get_supported_lr_schedulers()

or you can also search them with the filter(s).

from pytorch_optimizer import get_supported_lr_schedulers

get_supported_lr_schedulers('cosine*')
# ['cosine', 'cosine_annealing', 'cosine_annealing_with_warm_restart', 'cosine_annealing_with_warmup']

get_supported_lr_schedulers(['cosine*', '*warm*'])
# ['cosine', 'cosine_annealing', 'cosine_annealing_with_warm_restart', 'cosine_annealing_with_warmup', 'warmup_stable_decay']

LR Scheduler	Description	Official Code	Paper	Citation
Explore-Exploit	Wide-minima Density Hypothesis and the Explore-Exploit Learning Rate Schedule		https://arxiv.org/abs/2003.03977	cite
Chebyshev	Acceleration via Fractal Learning Rate Schedules		https://arxiv.org/abs/2103.01338	cite
REX	Revisiting Budgeted Training with an Improved Schedule	github	https://arxiv.org/abs/2107.04197	cite
WSD	Warmup-Stable-Decay learning rate scheduler	github	https://arxiv.org/abs/2404.06395	cite

Supported Loss Function

You can check the supported loss functions with below code.

from pytorch_optimizer import get_supported_loss_functions

supported_loss_functions = get_supported_loss_functions()

or you can also search them with the filter(s).

from pytorch_optimizer import get_supported_loss_functions

get_supported_loss_functions('*focal*')
# ['bcefocalloss', 'focalcosineloss', 'focalloss', 'focaltverskyloss']

get_supported_loss_functions(['*focal*', 'bce*'])
# ['bcefocalloss', 'bceloss', 'focalcosineloss', 'focalloss', 'focaltverskyloss']

Loss Functions	Description	Official Code	Paper	Citation
Label Smoothing	Rethinking the Inception Architecture for Computer Vision		https://arxiv.org/abs/1512.00567	cite
Focal	Focal Loss for Dense Object Detection		https://arxiv.org/abs/1708.02002	cite
Focal Cosine	Data-Efficient Deep Learning Method for Image Classification Using Data Augmentation, Focal Cosine Loss, and Ensemble		https://arxiv.org/abs/2007.07805	cite
LDAM	Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss	github	https://arxiv.org/abs/1906.07413	cite
Jaccard (IOU)	IoU Loss for 2D/3D Object Detection		https://arxiv.org/abs/1908.03851	cite
Bi-Tempered	The Principle of Unchanged Optimality in Reinforcement Learning Generalization		https://arxiv.org/abs/1906.03361	cite
Tversky	Tversky loss function for image segmentation using 3D fully convolutional deep networks		https://arxiv.org/abs/1706.05721	cite
Lovasz Hinge	A tractable surrogate for the optimization of the intersection-over-union measure in neural networks	github	https://arxiv.org/abs/1705.08790	cite

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	Improved bias-correction in Adam	Adaptive Gradient Norm Correction

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.

• code : github
• paper : arXiv

Gradient Centralization

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

• code : github
• paper : arXiv

Softplus Transformation

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

• paper : arXiv

Gradient Normalization

Norm Loss

• paper : arXiv

Positive-Negative Momentum

• code : github
• paper : arXiv

Linear learning rate warmup

• paper : arXiv

Stable weight decay

• code : github
• paper : arXiv

Explore-exploit learning rate schedule

• code : github
• paper : arXiv

Lookahead

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

Convergence issues can be fixed by endowing such algorithms with 'long-term memory' of past gradients.

Improved bias-correction in Adam

With the default bias-correction, Adam may actually make larger than requested gradient updates early in training.

Adaptive Gradient Norm Correction

Correcting the norm of a gradient in each iteration based on the adaptive training history of gradient norm.

Cautious optimizer

Updates only occur when the proposed update direction aligns with the current gradient.

Adam-ATAN2

Adam-atan2 is a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter.

Frequently asked questions

here

Visualization

here

Citation

Please cite the original authors of optimization algorithms. You can easily find it in the above table! If you use this software, please cite it below. Or you can get it from "cite this repository" button.

@software{Kim_pytorch_optimizer_optimizer_2021,
    author = {Kim, Hyeongchan},
    month = jan,
    title = {{pytorch_optimizer: optimizer & lr scheduler & loss function collections in PyTorch}},
    url = {https://github.com/kozistr/pytorch_optimizer},
    version = {3.1.0},
    year = {2021}
}

Maintainer

Hyeongchan Kim / @kozistr