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。
文章目录
1 简介2 结果A2GradExp(2018)A2GradInc(2018)A2GradUni(2018)AccSGD(2019)AdaBelief(2020)AdaBound(2019)AdaMod(2019)Adafactor(2018)AdamP(2020)AggMo(2019)Apollo(2020)DiffGrad*(2019)Lamb(2019)Lookahead*(2019)NovoGrad(2019)PID(2018)QHAdam(2019)QHM(2019)RAdam*(2019)Ranger(2019)RangerQH(2019)RangerVA(2019)SGDP(2020)SGDW(2017)SWATS(2017)Shampoo(2018)Yogi*(2018)AdamSGD
3 评价4 参考
1 简介
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。
optimizerpaperA2GradExphttps://arxiv.org/abs/1810.00553A2GradInchttps://arxiv.org/abs/1810.00553A2GradUnihttps://arxiv.org/abs/1810.00553AccSGDhttps://arxiv.org/abs/1803.05591AdaBeliefhttps://arxiv.org/abs/2010.07468AdaBoundhttps://arxiv.org/abs/1902.09843AdaModhttps://arxiv.org/abs/1910.12249Adafactorhttps://arxiv.org/abs/1804.04235AdamPhttps://arxiv.org/abs/2006.08217AggMohttps://arxiv.org/abs/1804.00325Apollohttps://arxiv.org/abs/2009.13586DiffGradhttps://arxiv.org/abs/1909.11015Lambhttps://arxiv.org/abs/1904.00962Lookaheadhttps://arxiv.org/abs/1907.08610NovoGradhttps://arxiv.org/abs/1905.11286PIDhttps://www4.comp.polyu.edu.hk/~cslzhang/paper/CVPR18_PID.pdfQHAdamhttps://arxiv.org/abs/1810.06801QHMhttps://arxiv.org/abs/1810.06801RAdamhttps://arxiv.org/abs/1908.03265Rangerhttps://arxiv.org/abs/1908.00700v2RangerQHhttps://arxiv.org/abs/1908.00700v2RangerVAhttps://arxiv.org/abs/1908.00700v2SGDPhttps://arxiv.org/abs/2006.08217SGDWhttps://arxiv.org/abs/1608.03983SWATShttps://arxiv.org/abs/1712.07628Shampoohttps://arxiv.org/abs/1802.09568Yogihttps://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：
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。
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。
2 结果
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*。
A2GradExp(2018)
Paper: Optimal Adaptive and Accelerated Stochastic Gradient Descent (2018)
rastriginrosenbrock
A2GradInc(2018)
Paper: Optimal Adaptive and Accelerated Stochastic Gradient Descent (2018)
rastriginrosenbrock
A2GradUni(2018)
Paper: Optimal Adaptive and Accelerated Stochastic Gradient Descent (2018)
rastriginrosenbrock
AccSGD(2019)
Paper: On the insufficiency of existing momentum schemes for Stochastic Optimization (2019)
rastriginrosenbrock
AdaBelief(2020)
Paper: AdaBelief Optimizer, adapting stepsizes by the belief in observed gradients (2020)
rastriginrosenbrock
AdaBound(2019)
Paper: An Adaptive and Momental Bound Method for Stochastic Learning. (2019)
rastriginrosenbrock
AdaMod(2019)
Paper: An Adaptive and Momental Bound Method for Stochastic Learning. (2019)
rastriginrosenbrock
Adafactor(2018)
Paper: Adafactor: Adaptive Learning Rates with Sublinear Memory Cost. (2018)
rastriginrosenbrock
AdamP(2020)
Paper: Slowing Down the Weight Norm Increase in Momentum-based Optimizers. (2020)
rastriginrosenbrock
AggMo(2019)
Paper: Aggregated Momentum: Stability Through Passive Damping. (2019)
rastriginrosenbrock
Apollo(2020)
Paper: Apollo: An Adaptive Parameter-wise Diagonal Quasi-Newton Method for Nonconvex Stochastic Optimization. (2020)
rastriginrosenbrock
DiffGrad*(2019)
Paper: diffGrad: An Optimization Method for Convolutional Neural Networks. (2019)
Reference Code: https://github.com/shivram1987/diffGrad
rastriginrosenbrock
Lamb(2019)
Paper: Large Batch Optimization for Deep Learning: Training BERT in 76 minutes (2019)
rastriginrosenbrock
Lookahead*(2019)
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
rastriginrosenbrock
NovoGrad(2019)
Paper: Stochastic Gradient Methods with Layer-wise Adaptive Moments for Training of Deep Networks (2019)
rastriginrosenbrock
PID(2018)
Paper: A PID Controller Approach for Stochastic Optimization of Deep Networks (2018)
rastriginrosenbrock
QHAdam(2019)
Paper: Quasi-hyperbolic momentum and Adam for deep learning (2019)
rastriginrosenbrock
QHM(2019)
Paper: Quasi-hyperbolic momentum and Adam for deep learning (2019)
rastriginrosenbrock
RAdam*(2019)
Paper: On the Variance of the Adaptive Learning Rate and Beyond (2019)
Reference Code: https://github.com/LiyuanLucasLiu/RAdam
rastriginrosenbrock
Ranger(2019)
Paper: Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM (2019)
rastriginrosenbrock
RangerQH(2019)
Paper: Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM (2019)
rastriginrosenbrock
RangerVA(2019)
Paper: Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM (2019)
rastriginrosenbrock
SGDP(2020)
Paper: Slowing Down the Weight Norm Increase in Momentum-based Optimizers. (2020)
rastriginrosenbrock
SGDW(2017)
Paper: SGDR: Stochastic Gradient Descent with Warm Restarts (2017)
rastriginrosenbrock
SWATS(2017)
Paper: Improving Generalization Performance by Switching from Adam to SGD (2017)
rastriginrosenbrock
Shampoo(2018)
Paper: Shampoo: Preconditioned Stochastic Tensor Optimization (2018)
rastriginrosenbrock
Yogi*(2018)
Paper: Adaptive Methods for Nonconvex Optimization (2018)
Reference Code: https://github.com/4rtemi5/Yogi-Optimizer_Keras
rastriginrosenbrock
Adam
pytorch自带
rastriginrosenbrock
SGD
pytorch自带
rastriginrosenbrock
3 评价
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：
AdamLookahead + (Adam or Yogi or RAdam)带有动量的SGDRAdam,Yogi,DiffGrad
4 参考
pytorch-optimizerpytorch如何看待最新提出的Rectified Adam (RAdam)？