AdaBelief Optimizer

NeurIPS 2020 Spotlight, trains fast as Adam, generalizes well as SGD, and is stable to train GANs.

Table of Contents

• External Links
• Installation and usage
• A quick look at the algorithm
• Discussions (IMPORTANT, please read before using)
• Reproduce results in the paper
• Citation

External Links

Project Page, arXiv , Reddit , Twitter

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

pip install adabelief-pytorch==0.0.5

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

Adabelief with Ranger optimizer

pip install ranger-adabelief==0.0.9

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

2. Tensorflow implementation

pip install adabelief-tf==0.0.1

from adabelief_tf impoty AdaBeliefOptimizer
optimizer = AdaBeliefOptimizer(learning_rate, epsilon=1e-12) 

A quick look at the algorithm

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 , where is the EMA (Exponential Moving Average) of ; in AdaBelief, the update direction is , where is the of . Intuitively, viewing as the prediction of , AdaBelief takes a large step when observation is close to prediction , and a small step when the observation greatly deviates from the prediction.

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 Recongnition

Results on GAN training

Results on LSTM

Results on Toy Example

Discussions

Installation

Please instal 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 algorithms

1. Weight Decay:

• Decoupling (argument weight_decouple (default:False) 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:
  

  If fixed_decay == False, the weight is multiplied by 1 -lr x weight_decay
  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.

• 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 and LSTM, it's set as 1e-12. We recommend try different epsilon values in practice, and sweep through a large region, e.g. 1e-8, 1e-10, 1e-12, 1e-14, 1e-16, 1e-18. Typically a smaller epsilon makes it more adaptive.

3. Rectify (argument rectify (default: False) 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.
  

Task	beta1	beta2	epsilon	weight_decay	weight_decouple	fixed_decay	rectify	amsgrad
Cifar	0.9	0.999	1e-8	5e-4	False	False	False	False
ImageNet	0.9	0.999	1e-8	1e-2	True	False	False	False
GAN	0.5	0.999	1e-12	0	False	False	False	False

• We also provide a modification of ranger optimizer in ranger-adavelief which combines RAdam + LookAhead + Gradient Centralization + AdaBelief, but this is not used in the paper and is not extensively tested.
• 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.

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. 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!

Citation

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