To add warm-up scheduler to optim (#60836)
Summary:
Warm up of learning rate scheduling has initially been discussed by Priya et. al. in the paper: https://arxiv.org/pdf/1706.02677.pdf .
In the section 2.2 of the paper they discussed and proposed idea of warming up learning schedulers in order to prevent big variance / noise in the learning rate. Then idea has been further discussed in the following papers:
* Akilesh Gotmare et al. https://arxiv.org/abs/1810.13243
* Bernstein et al http://proceedings.mlr.press/v80/bernstein18a/bernstein18a.pdf
* Liyuan Liu et al: https://arxiv.org/pdf/1908.03265.pdf
There are two type of popularly used learning rate warm up ideas
* Constant warmup (start with very small constant learning rate)
* Linear Warmup ( start with small learning rate and gradually increase)
In this PR we are adding warm up as learning rate scheduler. Note that learning rates are chainable, which means that we can merge warmup scheduler with any other learning rate scheduler to make more sophisticated learning rate scheduler.
## Linear Warmup
Linear Warmup is multiplying learning rate with pre-defined constant - warmup_factor in the first epoch (epoch 0). Then targeting to increase this multiplication constant to one in warmup_iters many epochs. Hence we can derive the formula at i-th step to have multiplication constant equal to:
warmup_factor + (1-warmup_factor) * i / warmup_iters
Moreover, the fraction of this quantity at point i to point i-1 will give us
1 + (1.0 - warmup_factor) / [warmup_iters*warmup_factor+(i-1)*(1-warmup_factor)]
which is used in get_lr() method in our implementation. Below we provide an example how to use linear warmup scheduler and to give an example to show how does it works.
```python
import torch
from torch.nn import Parameter
from torch.optim import SGD
from torch.optim.lr_scheduler import WarmUpLR
model = [Parameter(torch.randn(2, 2, requires_grad=True))]
optimizer = SGD(model, 0.1)
scheduler = WarmUpLR(optimizer, warmup_factor=0.1, warmup_iters=10, warmup_method="linear")
for epoch in range(15):
print(epoch, scheduler.get_last_lr()[0])
optimizer.step()
scheduler.step()
```
```
0 0.010000000000000002
1 0.019000000000000003
2 0.028000000000000008
3 0.03700000000000001
4 0.04600000000000001
5 0.055000000000000014
6 0.06400000000000002
7 0.07300000000000002
8 0.08200000000000003
9 0.09100000000000004
10 0.10000000000000005
11 0.10000000000000005
12 0.10000000000000005
13 0.10000000000000005
14 0.10000000000000005
```
## Constant Warmup
Constant warmup has straightforward idea, to multiply learning rate by warmup_factor until we reach to epoch warmup_factor, then do nothing for following epochs
```python
import torch
from torch.nn import Parameter
from torch.optim import SGD
from torch.optim.lr_scheduler import WarmUpLR
model = [Parameter(torch.randn(2, 2, requires_grad=True))]
optimizer = SGD(model, 0.1)
scheduler = WarmUpLR(optimizer, warmup_factor=0.1, warmup_iters=5, warmup_method="constant")
for epoch in range(10):
print(epoch, scheduler.get_last_lr()[0])
optimizer.step()
scheduler.step()
```
```
0 0.010000000000000002
1 0.010000000000000002
2 0.010000000000000002
3 0.010000000000000002
4 0.010000000000000002
5 0.10000000000000002
6 0.10000000000000002
7 0.10000000000000002
8 0.10000000000000002
9 0.10000000000000002
```
Pull Request resolved: https://github.com/pytorch/pytorch/pull/60836
Reviewed By: saketh-are
Differential Revision: D29537615
Pulled By: iramazanli
fbshipit-source-id: d910946027acc52663b301f9c56ade686e62cb69
