def testDefaultNoisyLinearCosine(self, serialize):
num_training_steps = 1000
initial_lr = 1.0
for step in range(0, 1500, 250):
# No numerical check because of noise
decayed_lr = learning_rate_schedule.NoisyLinearCosineDecay(
initial_lr, num_training_steps)
decayed_lr = _maybe_serialized(decayed_lr, serialize)
# Cannot be deterministically tested
self.evaluate(decayed_lr(step))
def testNonDefaultNoisyLinearCosine(self, serialize):
num_training_steps = 1000
initial_lr = 1.0
for step in range(0, 1500, 250):
# No numerical check because of noise
decayed_lr = learning_rate_schedule.NoisyLinearCosineDecay(
initial_lr,
num_training_steps,
initial_variance=0.5,
variance_decay=0.1,
alpha=0.1,
beta=1e-4,
num_periods=5)
decayed_lr = _maybe_serialized(decayed_lr, serialize)
# Cannot be deterministically tested
self.evaluate(decayed_lr(step))
def noisy_linear_cosine_decay(learning_rate,
global_step,
decay_steps,
initial_variance=1.0,
variance_decay=0.55,
num_periods=0.5,
alpha=0.0,
beta=0.001,
name=None):
"""Applies noisy 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 noisy 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 + eps_t) * cosine_decay + beta
decayed_learning_rate = learning_rate * decayed
```
where eps_t is 0-centered gaussian noise with variance
initial_variance / (1 + global_step) ** variance_decay
Example usage:
```python
decay_steps = 1000
lr_decayed = noisy_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.
initial_variance: initial variance for the noise. See computation above.
variance_decay: decay for the noise's variance. See computation above.
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
'NoisyLinearCosineDecay'.
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.NoisyLinearCosineDecay(
learning_rate,
decay_steps,
initial_variance=initial_variance,
variance_decay=variance_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
def noisy_linear_cosine_decay(learning_rate,
global_step,
decay_steps,
k_decay=1.0,
initial_variance=1.0,
variance_decay=0.55,
num_periods=0.5,
alpha=0.0,
beta=0.001,
name=None):
"""Applies noisy 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 noisy 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 + eps_t) * cosine_decay + beta
decayed_learning_rate = learning_rate * decayed
```
where eps_t is 0-centered gaussian noise with variance
initial_variance / (1 + global_step) ** variance_decay
Example usage:
```python
decay_steps = 1000
lr_decayed = noisy_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.
initial_variance: initial variance for the noise. See computation above.
variance_decay: decay for the noise's variance. See computation above.
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
'NoisyLinearCosineDecay'.
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.NoisyLinearCosineDecay(
learning_rate,
decay_steps,
k_decay=k_decay,
initial_variance=initial_variance,
variance_decay=variance_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
