本文主要展示各类深度学习优化器Optimizer的效果。所有结果基于pytorch实现，参考github项目pytorch-optimizer(仓库地址)的结果。pytorch-optimizer基于pytorch实现了常用的optimizer，非常推荐使用并加星该仓库。

pytorch-optimizer中所实现的optimizer及其文章主要如下所示。关于optimizer的优化研究非常多，但是不同任务，不同数据集所使用的optimizer效果都不一样，看看研究结果就行了。

optimizer	paper
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
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
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://arxiv.org/abs/1908.00700v2
RangerQH	https://arxiv.org/abs/1908.00700v2
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

为了评估不同optimizer的效果，pytorch-optimizer使用可视化方法来评估optimizer。可视化帮助我们了解不同的算法如何处理简单的情况，例如：鞍点，局部极小值，最低值等，并可能为算法的内部工作提供有趣的见解。pytorch-optimizer选择了Rosenbrock和Rastrigin 函数来进行可视化。具体如下：

1. Rosenbrock（也称为香蕉函数）是具有一个全局最小值(1.0,1.0)的非凸函数。整体最小值位于一个细长的，抛物线形的平坦山谷内。寻找山谷是微不足道的。但是，要收敛到全局最小值(1.0，1.0)是很困难的。优化算法可能会陷入局部最小值。

2. Rastrigin函数是非凸函数，并且在(0.0，0.0)中具有一个全局最小值。由于此函数的搜索空间很大且局部最小值很大，因此找到该函数的最小值是一个相当困难的工作。

下面分别显示不同年份算法在Rastrigin和Rosenbrock函数下的结果，结果显示为Rastrigin和Rosenbroc从上往下的投影图，其中绿色点表示最优点，结果坐标越接近绿色点表示optimizer效果越好。个人觉得效果较好的方法会在方法标题后加*。

Paper: Optimal Adaptive and Accelerated Stochastic Gradient Descent (2018)

rastrigin	rosenbrock

Paper: Optimal Adaptive and Accelerated Stochastic Gradient Descent (2018)

rastrigin	rosenbrock

Paper: Optimal Adaptive and Accelerated Stochastic Gradient Descent (2018)

rastrigin	rosenbrock

Paper: On the insufficiency of existing momentum schemes for Stochastic Optimization (2019)

rastrigin	rosenbrock

Paper: AdaBelief Optimizer, adapting stepsizes by the belief in observed gradients (2020)

rastrigin	rosenbrock

Paper: An Adaptive and Momental Bound Method for Stochastic Learning. (2019)

rastrigin	rosenbrock

Paper: An Adaptive and Momental Bound Method for Stochastic Learning. (2019)

rastrigin	rosenbrock

Paper: Adafactor: Adaptive Learning Rates with Sublinear Memory Cost. (2018)

rastrigin	rosenbrock

Paper: Slowing Down the Weight Norm Increase in Momentum-based Optimizers. (2020)

rastrigin	rosenbrock

Paper: Aggregated Momentum: Stability Through Passive Damping. (2019)

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Paper: Apollo: An Adaptive Parameter-wise Diagonal Quasi-Newton Method for Nonconvex Stochastic Optimization. (2020)

rastrigin	rosenbrock

Paper: diffGrad: An Optimization Method for Convolutional Neural Networks. (2019)

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

rastrigin	rosenbrock

Paper: Large Batch Optimization for Deep Learning: Training BERT in 76 minutes (2019)

rastrigin	rosenbrock

Paper: Lookahead Optimizer: k steps forward, 1 step back (2019)

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

非常需要注意的是Lookahead严格来说不算一种优化器，Lookahead需要一种其他优化器搭配工作，这里Lookahead搭配Yogi进行优化

rastrigin	rosenbrock

Paper: Stochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks (2019)

rastrigin	rosenbrock

Paper: A PID Controller Approach for Stochastic Optimization of Deep Networks (2018)

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Paper: Quasi-hyperbolic momentum and Adam for deep learning (2019)

rastrigin	rosenbrock

Paper: Quasi-hyperbolic momentum and Adam for deep learning (2019)

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Paper: On the Variance of the Adaptive Learning Rate and Beyond (2019)

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

rastrigin	rosenbrock

Paper: Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM (2019)

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Paper: Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM (2019)

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Paper: Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM (2019)

rastrigin	rosenbrock

Paper: Slowing Down the Weight Norm Increase in Momentum-based Optimizers. (2020)

rastrigin	rosenbrock

Paper: SGDR: Stochastic Gradient Descent with Warm Restarts (2017)

rastrigin	rosenbrock

Paper: Improving Generalization Performance by Switching from Adam to SGD (2017)

rastrigin	rosenbrock

Paper: Shampoo: Preconditioned Stochastic Tensor Optimization (2018)

rastrigin	rosenbrock

Paper: Adaptive Methods for Nonconvex Optimization (2018)

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

rastrigin	rosenbrock

pytorch自带

rastrigin	rosenbrock

pytorch自带

rastrigin	rosenbrock

看了第2节的结果，DiffGrad，Lookahead,RAdam,Yogi的结果应该还算不错。但是这种可视化结果并不完全正确，一方面训练的epoch太少，另外一方面数据不同以及学习率不同，结果也会大大不同。所以选择合适的优化器在实际调参中还是要具体应用。比如在这个可视化结果中，SGD和Adam效果一般，但是实际上SGD和Adam是广泛验证的优化器，各个任务都能获得不错的结果。SGD是著名的大后期选手，Adam无脑调参最优算法。RAdam很不错，但是并没有那么强，具体RAdam的评价见如何看待最新提出的Rectified Adam (RAdam)？。DiffGrad和Yogi某些任务不错，在某些任务可能效果更差，实际选择需要多次评估。Lookahead是Adam作者和Hinton联合推出的训练优化器，Lookahead可以配合多种优化器，好用是好用，可能没效果，但是一般都会有点提升，实际用Lookahead还是挺不错的。

结合可视化结果，实际下调参，先试试不同的学习率，然后再选择不同的优化器，如果不会调参，优化器个人推荐选择顺序如下：

1. Adam
2. Lookahead + (Adam or Yogi or RAdam)
3. 带有动量的SGD
4. RAdam,Yogi,DiffGrad

• pytorch-optimizer
• pytorch
• 如何看待最新提出的Rectified Adam (RAdam)？