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A collection of optimizers for Pytorch

A collection of optimizers for Pytorch

torch-optimizer

A collection of optimizers for Pytorch.

Simple example

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

Visualisations

Visualisations help us to see how different algorithms deals with simple situations like: saddle points, local minima, valleys etc, and may provide interesting insights into inner workings of algorithm. Rosenbrock and Rastrigin benchmark functions was selected, because:

  • Rosenbrock (also known as banana function), is non-convex function that has one global minima (1.0. 1.0). The global minimum is inside a long, narrow, parabolic shaped flat valley. To find the valley is trivial. To converge to the global minima, however, is difficult. Optimization algorithms might pay a lot of attention to one coordinate, and have problems to follow valley which is relatively flat.

  • Rastrigin function is a non-convex and has one global minima 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.

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

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

python examples/viz_optimizers.py

AccSGD

AccSGD

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

AdaBound

AdaBound

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

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.

AdaMod

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

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.

DiffGrad

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

LambV

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

NovoGrad

NovoGrad

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

PID

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

RAdam

RAdam

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

SGDW

SGDW

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://arxiv.org/abs/1608.03983

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.

Yogi

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

GitHub

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