def testDefaultDecay(self, serialize):
num_training_steps = 1000
initial_lr = 1.0
for step in range(0, 1500, 250):
decayed_lr = learning_rate_schedule.LinearCosineDecay(
initial_lr, num_training_steps)
decayed_lr = _maybe_serialized(decayed_lr, serialize)
expected = self.np_linear_cosine_decay(step, num_training_steps)
self.assertAllClose(self.evaluate(decayed_lr(step)), expected, 1e-6)
def linear_cosine_decay(learning_rate,
global_step,
decay_steps,
num_periods=0.5,
alpha=0.0,
beta=0.001,
name=None):
"""Applies linear cosine decay to the learning rate.
See [Bello et al., ICML2017] Neural Optimizer Search with RL.
https://arxiv.org/abs/1709.07417
For the idea of warm starts here controlled by `num_periods`,
see [Loshchilov & Hutter, ICLR2016] SGDR: Stochastic Gradient Descent
with Warm Restarts. https://arxiv.org/abs/1608.03983
Note that linear cosine decay is more aggressive than cosine decay and
larger initial learning rates can typically be used.
When training a model, it is often recommended to lower the learning rate as
the training progresses. This function applies a linear cosine decay function
to a provided initial learning rate. It requires a `global_step` value to
compute the decayed learning rate. You can just pass a TensorFlow variable
that you increment at each training step.
The function returns the decayed learning rate. It is computed as:
```python
global_step = min(global_step, decay_steps)
linear_decay = (decay_steps - global_step) / decay_steps)
cosine_decay = 0.5 * (
1 + cos(pi * 2 * num_periods * global_step / decay_steps))
decayed = (alpha + linear_decay) * cosine_decay + beta
decayed_learning_rate = learning_rate * decayed
```
Example usage:
```python
decay_steps = 1000
lr_decayed = linear_cosine_decay(learning_rate, global_step, decay_steps)
```
Args:
learning_rate: A scalar `float32` or `float64` Tensor or a Python number.
The initial learning rate.
global_step: A scalar `int32` or `int64` `Tensor` or a Python number. Global
step to use for the decay computation.
decay_steps: A scalar `int32` or `int64` `Tensor` or a Python number. Number
of steps to decay over.
num_periods: Number of periods in the cosine part of the decay. See
computation above.
alpha: See computation above.
beta: See computation above.
name: String. Optional name of the operation. Defaults to
'LinearCosineDecay'.
Returns:
A scalar `Tensor` of the same type as `learning_rate`. The decayed
learning rate.
Raises:
ValueError: if `global_step` is not supplied.
@compatibility(eager)
When eager execution is enabled, this function returns a function which in
turn returns the decayed learning rate Tensor. This can be useful for changing
the learning rate value across different invocations of optimizer functions.
@end_compatibility
"""
decayed_lr = learning_rate_schedule.LinearCosineDecay(
learning_rate,
decay_steps,
num_periods=num_periods,
alpha=alpha,
beta=beta,
name=name)
if not context.executing_eagerly():
decayed_lr = decayed_lr(global_step)
else:
decayed_lr = functools.partial(decayed_lr, global_step)
return decayed_lr
def linear_cosine_decay(learning_rate,
global_step,
decay_steps,
k_decay = 1.0,
num_periods=0.5,
alpha=0.0,
beta=0.001,
name=None):
"""Applies linear cosine decay to the learning rate.
Note that linear cosine decay is more aggressive than cosine decay and
larger initial learning rates can typically be used.
When training a model, it is often recommended to lower the learning rate as
the training progresses. This function applies a linear cosine decay function
to a provided initial learning rate. It requires a `global_step` value to
compute the decayed learning rate. You can just pass a TensorFlow variable
that you increment at each training step.
The function returns the decayed learning rate. It is computed as:
```python
global_step = min(global_step, decay_steps)
linear_decay = (decay_steps - global_step) / decay_steps)
cosine_decay = 0.5 * (
1 + cos(pi * 2 * num_periods * (global_step / decay_steps) ^ k_decay))
decayed = (alpha + linear_decay) * cosine_decay + beta
decayed_learning_rate = learning_rate * decayed
```
Example usage:
```python
decay_steps = 1000
lr_decayed = linear_cosine_decay(learning_rate, global_step, decay_steps)
```
Args:
learning_rate: A scalar `float32` or `float64` Tensor or a Python number.
The initial learning rate.
global_step: A scalar `int32` or `int64` `Tensor` or a Python number. Global
step to use for the decay computation.
decay_steps: A scalar `int32` or `int64` `Tensor` or a Python number. Number
of steps to decay over.
k_decay: A scalar `float32` or `float64` `Tensor` or a Python number. The k values of
the polynomial of k-decay method. Defaults to 1.0.
num_periods: Number of periods in the cosine part of the decay. See
computation above.
alpha: See computation above.
beta: See computation above.
name: String. Optional name of the operation. Defaults to
'LinearCosineDecay'.
Returns:
A scalar `Tensor` of the same type as `learning_rate`. The decayed
learning rate.
Raises:
ValueError: if `global_step` is not supplied.
References:
Neural Optimizer Search with Reinforcement Learning:
[Bello et al., 2017](http://proceedings.mlr.press/v70/bello17a.html)
([pdf](http://proceedings.mlr.press/v70/bello17a/bello17a.pdf))
Stochastic Gradient Descent with Warm Restarts:
[Loshchilov et al., 2017]
(https://openreview.net/forum?id=Skq89Scxx¬eId=Skq89Scxx)
([pdf](https://openreview.net/pdf?id=Skq89Scxx))
k-decay: A New Method For Learning Rate Schedule:
[Tao Zhang, Wei Li., 2020]
([pdf])(https://arxiv.org/abs/2004.05909)
@compatibility(eager)
When eager execution is enabled, this function returns a function which in
turn returns the decayed learning rate Tensor. This can be useful for changing
the learning rate value across different invocations of optimizer functions.
@end_compatibility
"""
decayed_lr = learning_rate_schedule.LinearCosineDecay(
learning_rate,
decay_steps,
k_decay=k_decay,
num_periods=num_periods,
alpha=alpha,
beta=beta,
name=name)
if not context.executing_eagerly():
decayed_lr = decayed_lr(global_step)
else:
decayed_lr = functools.partial(decayed_lr, global_step)
return decayed_lr
