Awesome

<h1 align="center">AdaBelief Optimizer</h1> <h3 align="center">NeurIPS 2020 Spotlight, trains fast as Adam, generalizes well as SGD, and is stable to train GANs.</h3>

Release of package

We have released adabelief-pytorch==0.2.0 and adabelief-tf==0.2.0. Please use the latest version from pip. Source code is available under folder pypi_packages/adabelief_pytorch0.2.0 and pypi_packages/adabelief_tf0.2.0.

External Links
Link to extra experiments
Table of hyper-parameters
Quick Guide Important infomation on hyper-params.
Installation and usage
A quick look at the algorithm
Detailed Discussions
Reproduce results in the paper
Update Plan
Citation
Slides

External Links

<a href="https://juntang-zhuang.github.io/adabelief/"> Project Page</a>, <a href="https://arxiv.org/abs/2010.07468"> arXiv </a>, <a href="https://www.reddit.com/r/MachineLearning/comments/jc1fp2/r_neurips_2020_spotlight_adabelief_optimizer">Reddit </a>, <a href="https://twitter.com/JuntangZhuang/status/1316934184607354891">Twitter</a>, <a href="https://www.bilibili.com/video/BV1uy4y1q7RG">BiliBili (中文)</a>, <a href="https://www.bilibili.com/video/BV1vi4y1c71S">BiliBili (Engligh)</a>, <a href="https://youtu.be/oGH7dmwvuaY">Youtube</a>

Link to code for extra experiments with AdaBelief

SN-GAN https://github.com/juntang-zhuang/SNGAN-AdaBelief
Transformer (PyTorch 1.1) https://github.com/juntang-zhuang/transformer-adabelief
Transformer (PyTorch 1.6) https://github.com/juntang-zhuang/fairseq-adabelief
Reinforcement Learning (Toy) https://github.com/juntang-zhuang/rainbow-adabelief
Reinforcement Learning (HalfCheetah-v2 Walker2d-v2) https://github.com/juntang-zhuang/SAC-Adabelief
Object detection (by yuanwei2019) https://github.com/yuanwei2019/EAdam-optimizer (Note that this version uses adabelief-pytorch==0.0.5, and the default hyper-parameters is different from adabelief-pytorch==0.1.0. Please check your version of adabelief, and whether you specify all hyper-parameters, or does the default is what you want.)
Text classification and word embedding in Tensorflow

Update for `adabelief-pytorch==0.2.0` (Crucial)

In the next release of adabelief-pytorch, we will modify the default of several arguments, in order to fit the needs of for general tasks such as GAN and Transformer. Please check if you specify these arguments or use the default when upgrade from version 0.0.5 to higher.

Version	epsilon	weight_decouple	rectify
adabelief-pytorch=0.0.5	1e-8	False	False
latest version 0.2.0>0.0.5	1e-16	True	True

Update for `adabelief-tf==0.2.0` (Crucial)

In adabelief-tf==0.1.0, we modify adabelief-tf to have the same feature as adabelief-pytorch, inlcuding decoupled weight decay and learning rate rectification. Furthermore, we will add support for TensorFlow>=2.0 and Keras. The source code is in pypi_packages/adabelief_tf0.1.0. We tested with a text classification task and a word embedding task. The default value is updated, please check if you specify these arguments or use the default when upgrade from version 0.0.1 to higher.:

Version	epsilon	weight_decouple	rectify
adabelief-tf=0.0.1	1e-8	Not supported	Not supported
latest version 0.2.0>0.0.1	1e-14	Supported (Not an option in arguments)	default: True

Quick Guide

Check if the code is from the latest official implementation (adabelief-pytorch==0.1.0, adabelief-tf==0.1.0) Default hyper-parameters are different from the old version.
check all hyper-parameters, DO NOT simply use the default,

Epsilon in AdaBelief is different from Adam (typically eps_adabelief = eps_adam*eps_adam) ( eps of Adam in Tensorflow is 1e-7, in PyTorch is 1e-8, need to consider this when use AdaBelief in Tensorflow) 

If SGD is better than Adam -> Set a large eps (1e-8) in AdaBelief-pytorch (1e-7 in Tensorflow ) If SGD is worse than Adam -> Set a small eps (1e-16) in AdaBelief-pytorch (1e-14 in Tensorflow, rectify=True often helps) 

If AdamW is better than Adam -> Turn on “weight_decouple” in AdaBelief-pytorch (this is on in adabelief-tf==0.1.0 and cannot shut down). Note that default weight decay is very different for Adam and AdamW, you might need to consider this when using AdaBelief with and without decoupled weight decay.
Check ALL hyper-parameters. Refer to our github page for a list of recommended hyper-parameters

Table of Hyper-parameters

Please check if you have specify all arguments and check your version is latest, the default might not be suitable for different tasks, see tables below

Hyper-parameters in PyTorch

Note weight decay varies with tasks, for different tasks the weight decay is untuned from the original repository (only changed the optimizer and other hyper-parameters).

Task	lr	beta1	beta2	epsilon	weight_decay	weight_decouple	rectify	fixed_decay	amsgrad
Cifar	1e-3	0.9	0.999	1e-8	5e-4	False	False	False	False
ImageNet	1e-3	0.9	0.999	1e-8	1e-2	True	False	False	False
Object detection (PASCAL)	1e-4	0.9	0.999	1e-8	1e-4	False	False	False	False
LSTM-1layer	1e-3	0.9	0.999	1e-16	1.2e-6	False	False	False	False
LSTM 2,3 layer	1e-2	0.9	0.999	1e-12	1.2e-6.	False	False	False	False
GAN (small)	2e-4	0.5	0.999	1e-12	0	True=False (decay=0)	False	False	False
SN-GAN (large)	2e-4	0.5	0.999	1e-16	0	True=False (decay=0)	True	False	False
Transformer	5e-4	0.9	0.999	1e-16	1e-4	True	True	False	False
Reinforcement (Rainbow)	1e-4	0.9	0.999	1e-10	0.0	True=False (decay=0)	True	False	False
Reinforcement (HalfCheetah-v2)	1e-3	0.9	0.999	1e-12	0.0	True=False (decay=0)	True	False	False

Hyper-parameters in Tensorflow (eps in Tensorflow might need to be larger than in PyTorch)

epsilon is used in a different way in Tensorflow (default 1e-7) compared to PyTorch (default 1e-8), so eps in Tensorflow might needs to be larger than in PyTorch (perhaps 100 times larger in Tensorflow, e.g. eps=1e-16 in PyTorch v.s eps=1e-14 in Tensorflow). But personally I don't have much experience with Tensorflow, it's likely that you need to slightly tune eps.

Installation and usage

1. PyTorch implementations

（ Results in the paper are all generated using the PyTorch implementation in adabelief-pytorch package, which is the ONLY package that I have extensively tested for now.)

AdaBelief

Please install latest version (0.2.0), previous version (0.0.5) uses different default arguments.

pip install adabelief-pytorch==0.2.0

from adabelief_pytorch import AdaBelief
optimizer = AdaBelief(model.parameters(), lr=1e-3, eps=1e-16, betas=(0.9,0.999), weight_decouple = True, rectify = False)

Adabelief with Ranger optimizer

pip install ranger-adabelief==0.1.0

from ranger_adabelief import RangerAdaBelief
optimizer = RangerAdaBelief(model.parameters(), lr=1e-3, eps=1e-12, betas=(0.9,0.999))

2. Tensorflow implementation (eps of AdaBelief in Tensorflow is larger than in PyTorch, same for Adam)

pip install adabelief-tf==0.2.0

from adabelief_tf import AdaBeliefOptimizer
optimizer = AdaBeliefOptimizer(learning_rate=1e-3, epsilon=1e-14, rectify=False)

<h2>A quick look at the algorithm</h2> <img src="imgs/adabelief-algo2.png" width="80%"> <div> Adam and AdaBelief are summarized in Algo.1 and Algo.2, where all operations are element-wise, with differences marked in blue. Note that no extra parameters are introduced in AdaBelief. For simplicity, we omit the bias correction step. Specifically, in Adam, the update direction is <img src="https://render.githubusercontent.com/render/math?math=\frac{m_t}{\sqrt{v_t}}"> , where <img src="https://render.githubusercontent.com/render/math?math=v_t"> is the EMA (Exponential Moving Average) of <img src="https://render.githubusercontent.com/render/math?math=g_t^2">; in AdaBelief, the update direction is <img src="https://render.githubusercontent.com/render/math?math=\frac{m_t}{\sqrt{s_t}}">, where <img src="https://render.githubusercontent.com/render/math?math=s_t"> is the of <img src="https://render.githubusercontent.com/render/math?math=(g_t-m_t)^2">. Intuitively, viewing <img src="https://render.githubusercontent.com/render/math?math=m_t"> as the prediction of <img src="https://render.githubusercontent.com/render/math?math=g_t">, AdaBelief takes a large step when observation <img src="https://render.githubusercontent.com/render/math?math=g_t"> is close to prediction <img src="https://render.githubusercontent.com/render/math?math=m_t">, and a small step when the observation greatly deviates from the prediction. </div>

Reproduce results in the paper

(Comparison with 8 other optimizers: SGD, Adam, AdaBound, RAdam, AdamW, Yogi, MSVAG, Fromage)

See folder PyTorch_Experiments, for each subfolder, execute sh run.sh. See readme.txt in each subfolder for visualization, or refer to jupyter notebook for visualization.

Results on Image Recognition

Results on GAN training

Results on a small GAN with vanilla CNN generator

Results on Spectral Normalization GAN with a ResNet generator

Results on LSTM

Results on Transformer

Results on Toy Example

Discussions

Installation

Please install the latest version from pip, old versions might suffer from bugs. Source code for up-to-date package is available in folder pypi_packages.

Discussion on hyper-parameters

AdaBelief uses a different denominator from Adam, and is orthogonal to other techniques such as recification, decoupled weight decay, weight averaging et.al. This implies when you use some techniques with Adam, to get a good result with AdaBelief you might still need those techniques.

epsilon in AdaBelief plays a different role as in Adam, typically when you use epslison=x in Adam, using epsilon=x*x will give similar results in AdaBelief. The default value epsilon=1e-8 is not a good option in many cases, in version >0.1.0 the default eps is set as 1e-16.
If you task needs a "non-adaptive" optimizer, which means SGD performs much better than Adam(W), such as on image recognition, you need to set a large epsilon(e.g. 1e-8) for AdaBelief to make it more non-adaptive; if your task needs a really adaptive optimizer, which means Adam is much better than SGD, such as GAN and Transformer, then the recommended epsilon for AdaBelief is small (1e-12, 1e-16 ...).
If decoupled weight decay is very important for your task, which means AdamW is much better than Adam, then you need to set weight_decouple as True to turn on decoupled decay in AdaBelief. Note that many optimizers uses decoupled weight decay without specifying it as an options, e.g. RAdam, but we provide it as an option so users are aware of what technique is actually used.
Don't use "gradient threshold" (clamp each element independently) in AdaBelief, it could result in division by 0 and explosion in update; but "gradient clip" (shrink amplitude of the gradient vector but keeps its direction) is fine, though from my limited experience sometimes the clip range needs to be the same or larger than Adam.

Discussion on algorithms

1. Weight Decay:

Decoupling (argument weight_decouple appears in AdaBelief and RangerAdaBelief): Currently there are two ways to perform weight decay for adaptive optimizers, directly apply it to the gradient (Adam), or decouple weight decay from gradient descent (AdamW). This is passed to the optimizer by argument weight_decouple (default: False).
Fixed ratio (argument fixed_decay (default: False) appears in AdaBelief): (1) If weight_decouple == False, then this argument does not affect optimization. (2) If weight_decouple == True: <ul> If fixed_decay == False, the weight is multiplied by 1 -lr x weight_decay </ul> <ul> If fixed_decay == True, the weight is multiplied by 1 - weight_decay. This is implemented as an option but not used to produce results in the paper. </ul>
What is the acutal weight-decay we are using? This is seldom discussed in the literature, but personally I think it's very important. When we set weight_decay=1e-4 for SGD, the weight is scaled by 1 - lr x weight_decay. Two points need to be emphasized: (1) lr in SGD is typically larger than Adam (0.1 vs 0.001), so the weight decay in Adam needs to be set as a larger number to compensate. (2) lr decays, this means typically we use a larger weight decay in early phases, and use a small weight decay in late phases.

2. Epsilon:

AdaBelief seems to require a different epsilon from Adam. In CV tasks in this paper, epsilon is set as 1e-8. For GAN training it's set as 1e-16. We recommend try different epsilon values in practice, and sweep through a large region. We recommend use eps=1e-8 when SGD outperforms Adam, such as many CV tasks; recommend eps=1e-16 when Adam outperforms SGD, such as GAN and Transformer. Sometimes you might need to try eps=1e-12, such as in some reinforcement learning tasks.

3. Rectify (argument `rectify` in `AdaBelief`):

Whether to turn on the rectification as in RAdam. The recitification basically uses SGD in early phases for warmup, then switch to Adam. Rectification is implemented as an option, but is never used to produce results in the paper.

4. AMSgrad (argument `amsgrad (default: False)` in `AdaBelief`):

Whether to take the max (over history) of denominator, same as AMSGrad. It's set as False for all experiments.

5. Details to reproduce results

Results in the paper are generated using the PyTorch implementation in adabelief-pytorch package. This is the ONLY package that I have extensively tested for now.
We also provide a modification of ranger optimizer in ranger-adabelief which combines RAdam + LookAhead + Gradient Centralization + AdaBelief, but this is not used in the paper and is not extensively tested.
<del> The adabelief-tf is a naive implementation in Tensorflow. It lacks many features such as decoupled weight decay, and is not extensively tested. Currently I don't have plans to improve it since I seldom use Tensorflow, please contact me if you want to collaborate and improve it.</del>
The adabelief-tf==0.1.0 supports the same feature as adabelief-pytorch==0.1.0, including decoupled weight decay and rectification. But personally I don't have the chance to perform extensive tests as with the PyTorch version.

6. Learning rate schedule

The experiments on Cifar is the same as demo in AdaBound, with the only difference is the optimizer. The ImageNet experiment uses a different learning rate schedule, typically is decayed by 1/10 at epoch 30, 60, and ends at 90. For some reasons I have not extensively experimented, AdaBelief performs good when decayed at epoch 70, 80 and ends at 90, using the default lr schedule produces a slightly worse result. If you have any ideas on this please open an issue here or email me.

7. Some experience with RNN

I got some feedbacks on RNN on reddit discussion, here are a few tips:

The epsilon is suggested to set as a smaller value for RNN (e.g. 1e-12, 1e-16). Please try different epsilon values, it varies from task to task.
I might confuse "gradient threshold" with "gradient clip" in previous readme, clarify below: (1) By "gradient threshold" I refer to element-wise operation, which only takes values between a certain region [a,b]. Values outside this region will be set as a and b respectively. (2) By "gradient clip" I refer to the operation on a vector or tensor. Suppose X is a tensor, if ||X|| > thres, then X <- X/||X|| * thres. Take X as a vector, "gradient clip" shrinks the amplitude but keeps the direction. (3) "Gradient threshold" is incompatible with AdaBelief, because if gt is thresholded for a long time, then |gt-mt|~=0, and the division will explode; however, "gradient clip" is fine for Adabelief, yet the clip range still needs tuning (perhaps AdaBelief needs a larger range than Adam).

8. Contact

Please contact me at j.zhuang@yale.edu or open an issue here if you would like to help improve it, especially the tensorflow version, or explore combination with other methods, some discussion on the theory part, or combination with other methods to create a better optimizer. Any thoughts are welcome!

Update Plan

To do

<del>Someone (under the wechat group Jiqizhixin) points out that the results on GAN is bad, this might be due to the choice of GAN model (We pick the simplest code example from PyTorch docs without adding more tricks), and we did not perform cherry-picking or worsen the baseline perfomance intentionally. We will update results on new GANs (e.g. SN-GAN) and release code later. </del>
<del> Upload code for LSTM experiments. </del>
<del> (10/23/2020) Transformer trains fine locally with PyTorch 1.1 CUDA9.0 (BLEU score 35.74 (highest is 35.85) on IWSLT14 DE-En with small transformer), but works much worse on a server with PyTorch 1.4 CUDA 10.0 (BLEU score < 26) using the same code. The code is to reproduce the error is at: https://github.com/juntang-zhuang/transformer-adabelief </del>
<del> Test AdaBelief on more examples, such as Transformer, Reinforcement Learning.</del>
<del> Merge Tensorflow improvements </del>
<del> Compare the rectified update, currently the implementation is slightly different from RAdam implementation.</del>
<del> Correct the coding error in RangerAdaBelief</del>
<del> The AMSGrad implmentation might be problematic, see discusssion https://github.com/juntang-zhuang/Adabelief-Optimizer/issues/32#issuecomment-742350592 </del>
<del> Coupled weight decay in adabelief-pytorch=0.1.0 is not working, though does not affect decoupled weight decay. https://github.com/juntang-zhuang/Adabelief-Optimizer/pull/33#issue-539128103 </del>
<del> Solve the problem in mixed-precision with AdaBelief, see discussion https://github.com/juntang-zhuang/Adabelief-Optimizer/issues/31#issue-759823121 </del>
Implement fused version (as in apex) for faster speed.

Done

Updated results on an SN-GAN is in https://github.com/juntang-zhuang/SNGAN-AdaBelief, AdaBelief achieves 12.36 FID (lower is better) on Cifar10, while Adam achieves 13.25 (number taken from the log of official repository PyTorch-studioGAN).
LSTM experiments uploaded to PyTorch_Experiments/LSTM
Identify the problem of Transformer with PyTorch 1.4, to be an old version fairseq is incompatible with new version PyTorch, works fine with latest fairseq. Code on Transformer to work with PyTorch 1.6 is at: https://github.com/juntang-zhuang/fairseq-adabelief Code for transformer to work with PyTorch 1.1 and CUDA9.0 is at: https://github.com/juntang-zhuang/transformer-adabelief
Tested on a toy example of reinforcement learning.
Released adabelief-pytorch==0.1.0 and adabelief-tf==0.1.0. The Tensorflow version now supports TF>=2.0 and Keras, with the same features as in the PyTorch version, including decoupled weight decay and rectification.
Released adabelief-pytorch==0.2.0. Fix the error with coupled weight decay in adabelief-pytorch==0.1.0, fix the amsgrad update in adabelief-pytorch==0.1.0. Add options to disable the message printing, by specify print_change_log=False when initiating the optimizer.
Released adabelief-tf==0.2.0. Add options to disable the message printing, by specify print_change_log=False when initiating the optimizer. Delte redundant computations, so 0.2.0 should be faster than 0.1.0. Removed dependencies on tensorflow-addons.
adabelief-pytorch==0.2.1 is compatible with mixed-precision training.

Citation

@article{zhuang2020adabelief,
  title={AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients},
  author={Zhuang, Juntang and Tang, Tommy and Ding, Yifan and Tatikonda, Sekhar and Dvornek, Nicha and Papademetris, Xenophon and Duncan, James},
  journal={Conference on Neural Information Processing Systems},
  year={2020}
}
@article{zhuang2021acprop,
  title={Momentum Centering and Asynchronous Update for Adaptive Gradient Methods},
  author={Zhuang, Juntang and Ding, Yifan and Tang, Tommy and Dvornek, Nicha and Tatikonda, Sekhar and Duncan, James},
  journal={Conference on Neural Information Processing Systems},
  year={2021}
}