torch-optimizer

torch-optimizer -- collection of optimizers for Pytorch

https://github.com/jettify/pytorch-optimizer

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torch-optimizer -- collection of optimizers for Pytorch

README.rst

torch-optimizer
===============
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**torch-optimizer** -- collection of optimizers for PyTorch_ compatible with optim_
module.


Simple example
--------------

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.DiffGrad(model.parameters(), lr=0.001)
    optimizer.step()


Installation
------------
Installation process is simple, just::

    $ pip install torch_optimizer


Documentation
-------------
https://pytorch-optimizer.rtfd.io


Citation
--------
Please cite the original authors of the optimization algorithms. If you like this
package::

    @software{Novik_torchoptimizers,
    	title        = {{torch-optimizer -- collection of optimization algorithms for PyTorch.}},
    	author       = {Novik, Mykola},
    	year         = 2020,
    	month        = 1,
    	version      = {1.0.1}
    }

Or use the github feature: "cite this repository" button.


Supported Optimizers
====================

+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `A2GradExp`_  | https://arxiv.org/abs/1810.00553                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `A2GradInc`_  | https://arxiv.org/abs/1810.00553                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `A2GradUni`_  | https://arxiv.org/abs/1810.00553                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `AccSGD`_     | https://arxiv.org/abs/1803.05591                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `AdaBelief`_  | https://arxiv.org/abs/2010.07468                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `AdaBound`_   | https://arxiv.org/abs/1902.09843                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `AdaMod`_     | https://arxiv.org/abs/1910.12249                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `Adafactor`_  | https://arxiv.org/abs/1804.04235                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `Adahessian`_ | https://arxiv.org/abs/2006.00719                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `AdamP`_      | https://arxiv.org/abs/2006.08217                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `AggMo`_      | https://arxiv.org/abs/1804.00325                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `Apollo`_     | https://arxiv.org/abs/2009.13586                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `DiffGrad`_   | https://arxiv.org/abs/1909.11015                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `Lamb`_       | https://arxiv.org/abs/1904.00962                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `Lookahead`_  | https://arxiv.org/abs/1907.08610                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `MADGRAD`_    | https://arxiv.org/abs/2101.11075                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `NovoGrad`_   | https://arxiv.org/abs/1905.11286                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `PID`_        | https://www4.comp.polyu.edu.hk/~cslzhang/paper/CVPR18_PID.pdf                                                                        |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `QHAdam`_     | https://arxiv.org/abs/1810.06801                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `QHM`_        | https://arxiv.org/abs/1810.06801                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `RAdam`_      | https://arxiv.org/abs/1908.03265                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `Ranger`_     | https://medium.com/@lessw/new-deep-learning-optimizer-ranger-synergistic-combination-of-radam-lookahead-for-the-best-of-2dc83f79a48d |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `RangerQH`_   | https://arxiv.org/abs/1810.06801                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `RangerVA`_   | https://arxiv.org/abs/1908.00700v2                                                                                                   |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `SGDP`_       | https://arxiv.org/abs/2006.08217                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `SGDW`_       | https://arxiv.org/abs/1608.03983                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `SWATS`_      | https://arxiv.org/abs/1712.07628                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `Shampoo`_    | https://arxiv.org/abs/1802.09568                                                                                                     |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+
|               |                                                                                                                                      |
| `Yogi`_       | https://papers.nips.cc/paper/8186-adaptive-methods-for-nonconvex-optimization                                                        |
+---------------+--------------------------------------------------------------------------------------------------------------------------------------+


Visualizations
--------------
Visualizations help us see how different algorithms deal with simple
situations like: saddle points, local minima, valleys etc, and may provide
interesting insights into the inner workings of an algorithm. Rosenbrock_ and Rastrigin_
benchmark_ functions were selected because:

* Rosenbrock_ (also known as banana function), is non-convex function that has
  one global minimum  `(1.0. 1.0)`. The global minimum is inside a long,
  narrow, parabolic shaped flat valley. Finding the valley is trivial. 
  Converging to the global minimum, however, is difficult. Optimization
  algorithms might pay a lot of attention to one coordinate, and struggle
  following the valley which is relatively flat.

 .. image::  https://upload.wikimedia.org/wikipedia/commons/3/32/Rosenbrock_function.svg

* Rastrigin_ is a non-convex function  and has one global minimum in `(0.0, 0.0)`.
  Finding the minimum of this function is a fairly difficult problem due to
  its large search space and its large number of local minima.

  .. image::  https://upload.wikimedia.org/wikipedia/commons/8/8b/Rastrigin_function.png

Each optimizer performs `501` optimization steps. Learning rate is the best one found
by a hyper parameter search algorithm, the rest of the tuning parameters are default. It
is very easy to extend the script and tune other optimizer parameters.


.. code::

    python examples/viz_optimizers.py


Warning
-------
Do not pick an optimizer based on visualizations, optimization approaches
have unique properties and may be tailored for different purposes or may
require explicit learning rate schedule etc. The best way to find out is to try 
one on your particular problem and see if it improves scores.

If you do not know which optimizer to use, start with the built in SGD/Adam. Once
the training logic is ready and baseline scores are established, swap the optimizer 
and see if there is any improvement.


A2GradExp
---------

+--------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_A2GradExp.png   |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_A2GradExp.png  |
+--------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.A2GradExp(
        model.parameters(),
        kappa=1000.0,
        beta=10.0,
        lips=10.0,
        rho=0.5,
    )
    optimizer.step()


**Paper**: *Optimal Adaptive and Accelerated Stochastic Gradient Descent* (2018) [https://arxiv.org/abs/1810.00553]

**Reference Code**: https://github.com/severilov/A2Grad_optimizer


A2GradInc
---------

+--------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_A2GradInc.png   |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_A2GradInc.png  |
+--------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.A2GradInc(
        model.parameters(),
        kappa=1000.0,
        beta=10.0,
        lips=10.0,
    )
    optimizer.step()


**Paper**: *Optimal Adaptive and Accelerated Stochastic Gradient Descent* (2018) [https://arxiv.org/abs/1810.00553]

**Reference Code**: https://github.com/severilov/A2Grad_optimizer


A2GradUni
---------

+--------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_A2GradUni.png   |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_A2GradUni.png  |
+--------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.A2GradUni(
        model.parameters(),
        kappa=1000.0,
        beta=10.0,
        lips=10.0,
    )
    optimizer.step()


**Paper**: *Optimal Adaptive and Accelerated Stochastic Gradient Descent* (2018) [https://arxiv.org/abs/1810.00553]

**Reference Code**: https://github.com/severilov/A2Grad_optimizer


AccSGD
------

+-----------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_AccSGD.png   |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_AccSGD.png  |
+-----------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.AccSGD(
        model.parameters(),
        lr=1e-3,
        kappa=1000.0,
        xi=10.0,
        small_const=0.7,
        weight_decay=0
    )
    optimizer.step()


**Paper**: *On the insufficiency of existing momentum schemes for Stochastic Optimization* (2019) [https://arxiv.org/abs/1803.05591]

**Reference Code**: https://github.com/rahulkidambi/AccSGD


AdaBelief
---------

+-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_AdaBelief.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_AdaBelief.png |
+-------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.AdaBelief(
        m.parameters(),
        lr= 1e-3,
        betas=(0.9, 0.999),
        eps=1e-3,
        weight_decay=0,
        amsgrad=False,
        weight_decouple=False,
        fixed_decay=False,
        rectify=False,
    )
    optimizer.step()


**Paper**: *AdaBelief Optimizer, adapting stepsizes by the belief in observed gradients* (2020) [https://arxiv.org/abs/2010.07468]

**Reference Code**: https://github.com/juntang-zhuang/Adabelief-Optimizer


AdaBound
--------

+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_AdaBound.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_AdaBound.png |
+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.AdaBound(
        m.parameters(),
        lr= 1e-3,
        betas= (0.9, 0.999),
        final_lr = 0.1,
        gamma=1e-3,
        eps= 1e-8,
        weight_decay=0,
        amsbound=False,
    )
    optimizer.step()


**Paper**: *Adaptive Gradient Methods with Dynamic Bound of Learning Rate* (2019) [https://arxiv.org/abs/1902.09843]

**Reference Code**: https://github.com/Luolc/AdaBound

AdaMod
------
The AdaMod method restricts the adaptive learning rates with adaptive and momental
upper bounds. The dynamic learning rate bounds are based on the exponential
moving averages of the adaptive learning rates themselves, which smooth out
unexpected large learning rates and stabilize the training of deep neural networks.

+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_AdaMod.png    |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_AdaMod.png   |
+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.AdaMod(
        m.parameters(),
        lr= 1e-3,
        betas=(0.9, 0.999),
        beta3=0.999,
        eps=1e-8,
        weight_decay=0,
    )
    optimizer.step()

**Paper**: *An Adaptive and Momental Bound Method for Stochastic Learning.* (2019) [https://arxiv.org/abs/1910.12249]

**Reference Code**: https://github.com/lancopku/AdaMod


Adafactor
---------
+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_Adafactor.png |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_Adafactor.png |
+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.Adafactor(
        m.parameters(),
        lr= 1e-3,
        eps2= (1e-30, 1e-3),
        clip_threshold=1.0,
        decay_rate=-0.8,
        beta1=None,
        weight_decay=0.0,
        scale_parameter=True,
        relative_step=True,
        warmup_init=False,
    )
    optimizer.step()

**Paper**: *Adafactor: Adaptive Learning Rates with Sublinear Memory Cost.* (2018) [https://arxiv.org/abs/1804.04235]

**Reference Code**: https://github.com/pytorch/fairseq/blob/master/fairseq/optim/adafactor.py


Adahessian
----------
+-------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_Adahessian.png |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_Adahessian.png  |
+-------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.Adahessian(
        m.parameters(),
        lr= 1.0,
        betas= (0.9, 0.999),
        eps= 1e-4,
        weight_decay=0.0,
        hessian_power=1.0,
    )
	  loss_fn(m(input), target).backward(create_graph = True) # create_graph=True is necessary for Hessian calculation
    optimizer.step()


**Paper**: *ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning* (2020) [https://arxiv.org/abs/2006.00719]

**Reference Code**: https://github.com/amirgholami/adahessian


AdamP
------
AdamP propose a simple and effective solution: at each iteration of the Adam optimizer
applied on scale-invariant weights (e.g., Conv weights preceding a BN layer), AdamP
removes the radial component (i.e., parallel to the weight vector) from the update vector.
Intuitively, this operation prevents the unnecessary update along the radial direction
that only increases the weight norm without contributing to the loss minimization.

+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_AdamP.png     |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_AdamP.png    |
+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.AdamP(
        m.parameters(),
        lr= 1e-3,
        betas=(0.9, 0.999),
        eps=1e-8,
        weight_decay=0,
        delta = 0.1,
        wd_ratio = 0.1
    )
    optimizer.step()

**Paper**: *Slowing Down the Weight Norm Increase in Momentum-based Optimizers.* (2020) [https://arxiv.org/abs/2006.08217]

**Reference Code**: https://github.com/clovaai/AdamP


AggMo
-----

+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_AggMo.png     |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_AggMo.png    |
+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.AggMo(
        m.parameters(),
        lr= 1e-3,
        betas=(0.0, 0.9, 0.99),
        weight_decay=0,
    )
    optimizer.step()

**Paper**: *Aggregated Momentum: Stability Through Passive Damping.* (2019) [https://arxiv.org/abs/1804.00325]

**Reference Code**: https://github.com/AtheMathmo/AggMo


Apollo
------

+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_Apollo.png    |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_Apollo.png   |
+------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.Apollo(
        m.parameters(),
        lr= 1e-2,
        beta=0.9,
        eps=1e-4,
        warmup=0,
        init_lr=0.01,
        weight_decay=0,
    )
    optimizer.step()

**Paper**: *Apollo: An Adaptive Parameter-wise Diagonal Quasi-Newton Method for Nonconvex Stochastic Optimization.* (2020) [https://arxiv.org/abs/2009.13586]

**Reference Code**: https://github.com/XuezheMax/apollo


DiffGrad
--------
Optimizer based on the difference between the present and the immediate past
gradient, the step size is adjusted for each parameter in such
a way that it should have a larger step size for faster gradient changing
parameters and a lower step size for lower gradient changing parameters.

+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_DiffGrad.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_DiffGrad.png  |
+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.DiffGrad(
        m.parameters(),
        lr= 1e-3,
        betas=(0.9, 0.999),
        eps=1e-8,
        weight_decay=0,
    )
    optimizer.step()


**Paper**: *diffGrad: An Optimization Method for Convolutional Neural Networks.* (2019) [https://arxiv.org/abs/1909.11015]

**Reference Code**: https://github.com/shivram1987/diffGrad

Lamb
----

+--------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_Lamb.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_Lamb.png  |
+--------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.Lamb(
        m.parameters(),
        lr= 1e-3,
        betas=(0.9, 0.999),
        eps=1e-8,
        weight_decay=0,
    )
    optimizer.step()


**Paper**: *Large Batch Optimization for Deep Learning: Training BERT in 76 minutes* (2019) [https://arxiv.org/abs/1904.00962]

**Reference Code**: https://github.com/cybertronai/pytorch-lamb

Lookahead
---------

+-----------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_LookaheadYogi.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_LookaheadYogi.png  |
+-----------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    # base optimizer, any other optimizer can be used like Adam or DiffGrad
    yogi = optim.Yogi(
        m.parameters(),
        lr= 1e-2,
        betas=(0.9, 0.999),
        eps=1e-3,
        initial_accumulator=1e-6,
        weight_decay=0,
    )

    optimizer = optim.Lookahead(yogi, k=5, alpha=0.5)
    optimizer.step()


**Paper**: *Lookahead Optimizer: k steps forward, 1 step back* (2019) [https://arxiv.org/abs/1907.08610]

**Reference Code**: https://github.com/alphadl/lookahead.pytorch


MADGRAD
---------

+-----------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_MADGRAD.png        |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_MADGRAD.png        |
+-----------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.MADGRAD(
        m.parameters(),
        lr=1e-2,
        momentum=0.9,
        weight_decay=0,
        eps=1e-6,
    )
    optimizer.step()


**Paper**: *Adaptivity without Compromise: A Momentumized, Adaptive, Dual Averaged Gradient Method for Stochastic Optimization* (2021) [https://arxiv.org/abs/2101.11075]

**Reference Code**: https://github.com/facebookresearch/madgrad


NovoGrad
--------

+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_NovoGrad.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_NovoGrad.png  |
+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.NovoGrad(
        m.parameters(),
        lr= 1e-3,
        betas=(0.9, 0.999),
        eps=1e-8,
        weight_decay=0,
        grad_averaging=False,
        amsgrad=False,
    )
    optimizer.step()


**Paper**: *Stochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks* (2019) [https://arxiv.org/abs/1905.11286]

**Reference Code**: https://github.com/NVIDIA/DeepLearningExamples/


PID
---

+-------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_PID.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_PID.png  |
+-------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.PID(
        m.parameters(),
        lr=1e-3,
        momentum=0,
        dampening=0,
        weight_decay=1e-2,
        integral=5.0,
        derivative=10.0,
    )
    optimizer.step()


**Paper**: *A PID Controller Approach for Stochastic Optimization of Deep Networks* (2018) [http://www4.comp.polyu.edu.hk/~cslzhang/paper/CVPR18_PID.pdf]

**Reference Code**: https://github.com/tensorboy/PIDOptimizer


QHAdam
------

+----------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_QHAdam.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_QHAdam.png  |
+----------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.QHAdam(
        m.parameters(),
        lr= 1e-3,
        betas=(0.9, 0.999),
        nus=(1.0, 1.0),
        weight_decay=0,
        decouple_weight_decay=False,
        eps=1e-8,
    )
    optimizer.step()


**Paper**: *Quasi-hyperbolic momentum and Adam for deep learning* (2019) [https://arxiv.org/abs/1810.06801]

**Reference Code**: https://github.com/facebookresearch/qhoptim


QHM
---

+-------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_QHM.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_QHM.png  |
+-------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.QHM(
        m.parameters(),
        lr=1e-3,
        momentum=0,
        nu=0.7,
        weight_decay=1e-2,
        weight_decay_type='grad',
    )
    optimizer.step()


**Paper**: *Quasi-hyperbolic momentum and Adam for deep learning* (2019) [https://arxiv.org/abs/1810.06801]

**Reference Code**: https://github.com/facebookresearch/qhoptim


RAdam
-----

+---------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_RAdam.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_RAdam.png  |
+---------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------+

Deprecated, please use version provided by PyTorch_.

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.RAdam(
        m.parameters(),
        lr= 1e-3,
        betas=(0.9, 0.999),
        eps=1e-8,
        weight_decay=0,
    )
    optimizer.step()


**Paper**: *On the Variance of the Adaptive Learning Rate and Beyond* (2019) [https://arxiv.org/abs/1908.03265]

**Reference Code**: https://github.com/LiyuanLucasLiu/RAdam


Ranger
------

+----------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_Ranger.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_Ranger.png  |
+----------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.Ranger(
        m.parameters(),
        lr=1e-3,
        alpha=0.5,
        k=6,
        N_sma_threshhold=5,
        betas=(.95, 0.999),
        eps=1e-5,
        weight_decay=0
    )
    optimizer.step()


**Paper**: *New Deep Learning Optimizer, Ranger: Synergistic combination of RAdam + LookAhead for the best of both* (2019) [https://medium.com/@lessw/new-deep-learning-optimizer-ranger-synergistic-combination-of-radam-lookahead-for-the-best-of-2dc83f79a48d]

**Reference Code**: https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer


RangerQH
--------

+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_RangerQH.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_RangerQH.png  |
+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.RangerQH(
        m.parameters(),
        lr=1e-3,
        betas=(0.9, 0.999),
        nus=(.7, 1.0),
        weight_decay=0.0,
        k=6,
        alpha=.5,
        decouple_weight_decay=False,
        eps=1e-8,
    )
    optimizer.step()


**Paper**: *Quasi-hyperbolic momentum and Adam for deep learning* (2018) [https://arxiv.org/abs/1810.06801]

**Reference Code**: https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer


RangerVA
--------

+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_RangerVA.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_RangerVA.png  |
+------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.RangerVA(
        m.parameters(),
        lr=1e-3,
        alpha=0.5,
        k=6,
        n_sma_threshhold=5,
        betas=(.95, 0.999),
        eps=1e-5,
        weight_decay=0,
        amsgrad=True,
        transformer='softplus',
        smooth=50,
        grad_transformer='square'
    )
    optimizer.step()


**Paper**: *Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM* (2019) [https://arxiv.org/abs/1908.00700v2]

**Reference Code**: https://github.com/lessw2020/Ranger-Deep-Learning-Optimizer


SGDP
----

+--------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_SGDP.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_SGDP.png  |
+--------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.SGDP(
        m.parameters(),
        lr= 1e-3,
        momentum=0,
        dampening=0,
        weight_decay=1e-2,
        nesterov=False,
        delta = 0.1,
        wd_ratio = 0.1
    )
    optimizer.step()


**Paper**: *Slowing Down the Weight Norm Increase in Momentum-based Optimizers.* (2020) [https://arxiv.org/abs/2006.08217]

**Reference Code**: https://github.com/clovaai/AdamP


SGDW
----

+--------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_SGDW.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_SGDW.png  |
+--------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.SGDW(
        m.parameters(),
        lr= 1e-3,
        momentum=0,
        dampening=0,
        weight_decay=1e-2,
        nesterov=False,
    )
    optimizer.step()


**Paper**: *SGDR: Stochastic Gradient Descent with Warm Restarts* (2017) [https://arxiv.org/abs/1608.03983]

**Reference Code**: https://github.com/pytorch/pytorch/pull/22466


SWATS
-----

+---------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_SWATS.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_SWATS.png  |
+---------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.SWATS(
        model.parameters(),
        lr=1e-1,
        betas=(0.9, 0.999),
        eps=1e-3,
        weight_decay= 0.0,
        amsgrad=False,
        nesterov=False,
    )
    optimizer.step()


**Paper**: *Improving Generalization Performance by Switching from Adam to SGD* (2017) [https://arxiv.org/abs/1712.07628]

**Reference Code**: https://github.com/Mrpatekful/swats


Shampoo
-------

+-----------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_Shampoo.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_Shampoo.png  |
+-----------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.Shampoo(
        m.parameters(),
        lr=1e-1,
        momentum=0.0,
        weight_decay=0.0,
        epsilon=1e-4,
        update_freq=1,
    )
    optimizer.step()


**Paper**: *Shampoo: Preconditioned Stochastic Tensor Optimization* (2018) [https://arxiv.org/abs/1802.09568]

**Reference Code**: https://github.com/moskomule/shampoo.pytorch


Yogi
----

Yogi is optimization algorithm based on ADAM with more fine grained effective
learning rate control, and has similar theoretical guarantees on convergence as ADAM.

+--------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_Yogi.png  |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_Yogi.png  |
+--------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+

.. code:: python

    import torch_optimizer as optim

    # model = ...
    optimizer = optim.Yogi(
        m.parameters(),
        lr= 1e-2,
        betas=(0.9, 0.999),
        eps=1e-3,
        initial_accumulator=1e-6,
        weight_decay=0,
    )
    optimizer.step()


**Paper**: *Adaptive Methods for Nonconvex Optimization* (2018) [https://papers.nips.cc/paper/8186-adaptive-methods-for-nonconvex-optimization]

**Reference Code**: https://github.com/4rtemi5/Yogi-Optimizer_Keras


Adam (PyTorch built-in)
-----------------------

+---------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_Adam.png   |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_Adam.png  |
+---------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------------------+

SGD (PyTorch built-in)
----------------------

+--------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+
| .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rastrigin_SGD.png   |  .. image:: https://raw.githubusercontent.com/jettify/pytorch-optimizer/master/docs/rosenbrock_SGD.png  |
+--------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+

.. _Python: https://www.python.org
.. _PyTorch: https://github.com/pytorch/pytorch
.. _Rastrigin: https://en.wikipedia.org/wiki/Rastrigin_function
.. _Rosenbrock: https://en.wikipedia.org/wiki/Rosenbrock_function
.. _benchmark: https://en.wikipedia.org/wiki/Test_functions_for_optimization
.. _optim: https://pytorch.org/docs/stable/optim.html

Owner

Citation (CITATION.cff)

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
  - family-names: Novik
    given-names: Mykola
    orcid: https://orcid.org/0000-0002-0890-1159
title: "torch-optimizer -- collection of optimization algorithms for PyTorch."
version: 1.0.1
date-released: 2020-01-11

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