Module keras.optimizer_v2.ftrl
Ftrl-proximal optimizer implementation.
Expand source code
# Copyright 2018 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Ftrl-proximal optimizer implementation."""
import tensorflow.compat.v2 as tf
# pylint: disable=g-classes-have-attributes
from keras.optimizer_v2 import optimizer_v2
from tensorflow.python.util.tf_export import keras_export
@keras_export('keras.optimizers.Ftrl')
class Ftrl(optimizer_v2.OptimizerV2):
r"""Optimizer that implements the FTRL algorithm.
"Follow The Regularized Leader" (FTRL) is an optimization algorithm developed
at Google for click-through rate prediction in the early 2010s. It is most
suitable for shallow models with large and sparse feature spaces.
The algorithm is described by
[McMahan et al., 2013](https://research.google.com/pubs/archive/41159.pdf).
The Keras version has support for both online L2 regularization
(the L2 regularization described in the paper
above) and shrinkage-type L2 regularization
(which is the addition of an L2 penalty to the loss function).
Initialization:
```python
n = 0
sigma = 0
z = 0
```
Update rule for one variable `w`:
```python
prev_n = n
n = n + g ** 2
sigma = (sqrt(n) - sqrt(prev_n)) / lr
z = z + g - sigma * w
if abs(z) < lambda_1:
w = 0
else:
w = (sgn(z) * lambda_1 - z) / ((beta + sqrt(n)) / alpha + lambda_2)
```
Notation:
- `lr` is the learning rate
- `g` is the gradient for the variable
- `lambda_1` is the L1 regularization strength
- `lambda_2` is the L2 regularization strength
Check the documentation for the `l2_shrinkage_regularization_strength`
parameter for more details when shrinkage is enabled, in which case gradient
is replaced with a gradient with shrinkage.
Args:
learning_rate: A `Tensor`, floating point value, or a schedule that is a
`tf.keras.optimizers.schedules.LearningRateSchedule`. The learning rate.
learning_rate_power: A float value, must be less or equal to zero.
Controls how the learning rate decreases during training. Use zero for
a fixed learning rate.
initial_accumulator_value: The starting value for accumulators.
Only zero or positive values are allowed.
l1_regularization_strength: A float value, must be greater than or
equal to zero. Defaults to 0.0.
l2_regularization_strength: A float value, must be greater than or
equal to zero. Defaults to 0.0.
name: Optional name prefix for the operations created when applying
gradients. Defaults to `"Ftrl"`.
l2_shrinkage_regularization_strength: A float value, must be greater than
or equal to zero. This differs from L2 above in that the L2 above is a
stabilization penalty, whereas this L2 shrinkage is a magnitude penalty.
When input is sparse shrinkage will only happen on the active weights.
beta: A float value, representing the beta value from the paper.
Defaults to 0.0.
**kwargs: Keyword arguments. Allowed to be one of
`"clipnorm"` or `"clipvalue"`.
`"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
gradients by value.
Reference:
- [McMahan et al., 2013](
https://research.google.com/pubs/archive/41159.pdf)
"""
def __init__(self,
learning_rate=0.001,
learning_rate_power=-0.5,
initial_accumulator_value=0.1,
l1_regularization_strength=0.0,
l2_regularization_strength=0.0,
name='Ftrl',
l2_shrinkage_regularization_strength=0.0,
beta=0.0,
**kwargs):
super(Ftrl, self).__init__(name, **kwargs)
if initial_accumulator_value < 0.0:
raise ValueError(
'initial_accumulator_value %f needs to be positive or zero' %
initial_accumulator_value)
if learning_rate_power > 0.0:
raise ValueError('learning_rate_power %f needs to be negative or zero' %
learning_rate_power)
if l1_regularization_strength < 0.0:
raise ValueError(
'l1_regularization_strength %f needs to be positive or zero' %
l1_regularization_strength)
if l2_regularization_strength < 0.0:
raise ValueError(
'l2_regularization_strength %f needs to be positive or zero' %
l2_regularization_strength)
if l2_shrinkage_regularization_strength < 0.0:
raise ValueError(
'l2_shrinkage_regularization_strength %f needs to be positive'
' or zero' % l2_shrinkage_regularization_strength)
self._set_hyper('learning_rate', learning_rate)
self._set_hyper('decay', self._initial_decay)
self._set_hyper('learning_rate_power', learning_rate_power)
self._set_hyper('l1_regularization_strength', l1_regularization_strength)
self._set_hyper('l2_regularization_strength', l2_regularization_strength)
self._set_hyper('beta', beta)
self._initial_accumulator_value = initial_accumulator_value
self._l2_shrinkage_regularization_strength = (
l2_shrinkage_regularization_strength)
def _create_slots(self, var_list):
# Create the "accum" and "linear" slots.
for var in var_list:
dtype = var.dtype.base_dtype
init = tf.compat.v1.constant_initializer(
self._initial_accumulator_value, dtype=dtype)
self.add_slot(var, 'accumulator', init)
self.add_slot(var, 'linear')
def _prepare_local(self, var_device, var_dtype, apply_state):
super(Ftrl, self)._prepare_local(var_device, var_dtype, apply_state)
apply_state[(var_device, var_dtype)].update(
dict(
learning_rate_power=tf.identity(
self._get_hyper('learning_rate_power', var_dtype)),
l1_regularization_strength=tf.identity(
self._get_hyper('l1_regularization_strength', var_dtype)),
l2_regularization_strength=tf.identity(
self._get_hyper('l2_regularization_strength', var_dtype)),
beta=tf.identity(self._get_hyper('beta', var_dtype)),
l2_shrinkage_regularization_strength=tf.cast(
self._l2_shrinkage_regularization_strength, var_dtype)))
def _resource_apply_dense(self, grad, var, apply_state=None):
var_device, var_dtype = var.device, var.dtype.base_dtype
coefficients = ((apply_state or {}).get((var_device, var_dtype))
or self._fallback_apply_state(var_device, var_dtype))
# Adjust L2 regularization strength to include beta to avoid the underlying
# TensorFlow ops needing to include it.
adjusted_l2_regularization_strength = (
coefficients['l2_regularization_strength'] + coefficients['beta'] /
(2. * coefficients['lr_t']))
accum = self.get_slot(var, 'accumulator')
linear = self.get_slot(var, 'linear')
if self._l2_shrinkage_regularization_strength <= 0.0:
return tf.raw_ops.ResourceApplyFtrl(
var=var.handle,
accum=accum.handle,
linear=linear.handle,
grad=grad,
lr=coefficients['lr_t'],
l1=coefficients['l1_regularization_strength'],
l2=adjusted_l2_regularization_strength,
lr_power=coefficients['learning_rate_power'],
use_locking=self._use_locking)
else:
return tf.raw_ops.ResourceApplyFtrlV2(
var=var.handle,
accum=accum.handle,
linear=linear.handle,
grad=grad,
lr=coefficients['lr_t'],
l1=coefficients['l1_regularization_strength'],
l2=adjusted_l2_regularization_strength,
l2_shrinkage=coefficients['l2_shrinkage_regularization_strength'],
lr_power=coefficients['learning_rate_power'],
use_locking=self._use_locking)
def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
var_device, var_dtype = var.device, var.dtype.base_dtype
coefficients = ((apply_state or {}).get((var_device, var_dtype))
or self._fallback_apply_state(var_device, var_dtype))
# Adjust L2 regularization strength to include beta to avoid the underlying
# TensorFlow ops needing to include it.
adjusted_l2_regularization_strength = (
coefficients['l2_regularization_strength'] + coefficients['beta'] /
(2. * coefficients['lr_t']))
accum = self.get_slot(var, 'accumulator')
linear = self.get_slot(var, 'linear')
if self._l2_shrinkage_regularization_strength <= 0.0:
return tf.raw_ops.ResourceSparseApplyFtrl(
var=var.handle,
accum=accum.handle,
linear=linear.handle,
grad=grad,
indices=indices,
lr=coefficients['lr_t'],
l1=coefficients['l1_regularization_strength'],
l2=adjusted_l2_regularization_strength,
lr_power=coefficients['learning_rate_power'],
use_locking=self._use_locking)
else:
return tf.raw_ops.ResourceSparseApplyFtrlV2(
var=var.handle,
accum=accum.handle,
linear=linear.handle,
grad=grad,
indices=indices,
lr=coefficients['lr_t'],
l1=coefficients['l1_regularization_strength'],
l2=adjusted_l2_regularization_strength,
l2_shrinkage=coefficients['l2_shrinkage_regularization_strength'],
lr_power=coefficients['learning_rate_power'],
use_locking=self._use_locking)
def get_config(self):
config = super(Ftrl, self).get_config()
config.update({
'learning_rate':
self._serialize_hyperparameter('learning_rate'),
'decay':
self._initial_decay,
'initial_accumulator_value':
self._initial_accumulator_value,
'learning_rate_power':
self._serialize_hyperparameter('learning_rate_power'),
'l1_regularization_strength':
self._serialize_hyperparameter('l1_regularization_strength'),
'l2_regularization_strength':
self._serialize_hyperparameter('l2_regularization_strength'),
'beta':
self._serialize_hyperparameter('beta'),
'l2_shrinkage_regularization_strength':
self._l2_shrinkage_regularization_strength,
})
return config
Classes
class Ftrl (learning_rate=0.001, learning_rate_power=-0.5, initial_accumulator_value=0.1, l1_regularization_strength=0.0, l2_regularization_strength=0.0, name='Ftrl', l2_shrinkage_regularization_strength=0.0, beta=0.0, **kwargs)
-
Optimizer that implements the FTRL algorithm.
"Follow The Regularized Leader" (FTRL) is an optimization algorithm developed at Google for click-through rate prediction in the early 2010s. It is most suitable for shallow models with large and sparse feature spaces. The algorithm is described by McMahan et al., 2013. The Keras version has support for both online L2 regularization (the L2 regularization described in the paper above) and shrinkage-type L2 regularization (which is the addition of an L2 penalty to the loss function).
Initialization:
n = 0 sigma = 0 z = 0
Update rule for one variable
w
:prev_n = n n = n + g ** 2 sigma = (sqrt(n) - sqrt(prev_n)) / lr z = z + g - sigma * w if abs(z) < lambda_1: w = 0 else: w = (sgn(z) * lambda_1 - z) / ((beta + sqrt(n)) / alpha + lambda_2)
Notation:
lr
is the learning rateg
is the gradient for the variablelambda_1
is the L1 regularization strengthlambda_2
is the L2 regularization strength
Check the documentation for the
l2_shrinkage_regularization_strength
parameter for more details when shrinkage is enabled, in which case gradient is replaced with a gradient with shrinkage.Args
learning_rate
- A
Tensor
, floating point value, or a schedule that is atf.keras.optimizers.schedules.LearningRateSchedule
. The learning rate. learning_rate_power
- A float value, must be less or equal to zero. Controls how the learning rate decreases during training. Use zero for a fixed learning rate.
initial_accumulator_value
- The starting value for accumulators. Only zero or positive values are allowed.
l1_regularization_strength
- A float value, must be greater than or equal to zero. Defaults to 0.0.
l2_regularization_strength
- A float value, must be greater than or equal to zero. Defaults to 0.0.
name
- Optional name prefix for the operations created when applying
gradients.
Defaults to
"Ftrl"
. l2_shrinkage_regularization_strength
- A float value, must be greater than or equal to zero. This differs from L2 above in that the L2 above is a stabilization penalty, whereas this L2 shrinkage is a magnitude penalty. When input is sparse shrinkage will only happen on the active weights.
beta
- A float value, representing the beta value from the paper. Defaults to 0.0.
**kwargs
- Keyword arguments. Allowed to be one of
"clipnorm"
or"clipvalue"
."clipnorm"
(float) clips gradients by norm;"clipvalue"
(float) clips gradients by value.
Reference
Create a new Optimizer.
This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.
This class is stateful and thread-compatible.
Example of custom gradient transformations:
def my_gradient_transformer(grads_and_vars): # Simple example, double the gradients. return [(2. * g, v) for g, v in grads_and_vars] optimizer = tf.keras.optimizers.SGD( 1e-3, gradient_transformers=[my_gradient_transformer])
Args
name
- String. The name to use for momentum accumulator weights created by the optimizer.
gradient_aggregator
- The function to use to aggregate gradients across
devices (when using
tf.distribute.Strategy
). IfNone
, defaults to summing the gradients across devices. The function should accept and return a list of(gradient, variable)
tuples. gradient_transformers
- Optional. List of functions to use to transform
gradients before applying updates to Variables. The functions are
applied after
gradient_aggregator
. The functions should accept and return a list of(gradient, variable)
tuples. **kwargs
- keyword arguments. Allowed arguments are
clipvalue
,clipnorm
,global_clipnorm
. Ifclipvalue
(float) is set, the gradient of each weight is clipped to be no higher than this value. Ifclipnorm
(float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. Ifglobal_clipnorm
(float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.
Raises
ValueError
- in case of any invalid argument.
Expand source code
class Ftrl(optimizer_v2.OptimizerV2): r"""Optimizer that implements the FTRL algorithm. "Follow The Regularized Leader" (FTRL) is an optimization algorithm developed at Google for click-through rate prediction in the early 2010s. It is most suitable for shallow models with large and sparse feature spaces. The algorithm is described by [McMahan et al., 2013](https://research.google.com/pubs/archive/41159.pdf). The Keras version has support for both online L2 regularization (the L2 regularization described in the paper above) and shrinkage-type L2 regularization (which is the addition of an L2 penalty to the loss function). Initialization: ```python n = 0 sigma = 0 z = 0 ``` Update rule for one variable `w`: ```python prev_n = n n = n + g ** 2 sigma = (sqrt(n) - sqrt(prev_n)) / lr z = z + g - sigma * w if abs(z) < lambda_1: w = 0 else: w = (sgn(z) * lambda_1 - z) / ((beta + sqrt(n)) / alpha + lambda_2) ``` Notation: - `lr` is the learning rate - `g` is the gradient for the variable - `lambda_1` is the L1 regularization strength - `lambda_2` is the L2 regularization strength Check the documentation for the `l2_shrinkage_regularization_strength` parameter for more details when shrinkage is enabled, in which case gradient is replaced with a gradient with shrinkage. Args: learning_rate: A `Tensor`, floating point value, or a schedule that is a `tf.keras.optimizers.schedules.LearningRateSchedule`. The learning rate. learning_rate_power: A float value, must be less or equal to zero. Controls how the learning rate decreases during training. Use zero for a fixed learning rate. initial_accumulator_value: The starting value for accumulators. Only zero or positive values are allowed. l1_regularization_strength: A float value, must be greater than or equal to zero. Defaults to 0.0. l2_regularization_strength: A float value, must be greater than or equal to zero. Defaults to 0.0. name: Optional name prefix for the operations created when applying gradients. Defaults to `"Ftrl"`. l2_shrinkage_regularization_strength: A float value, must be greater than or equal to zero. This differs from L2 above in that the L2 above is a stabilization penalty, whereas this L2 shrinkage is a magnitude penalty. When input is sparse shrinkage will only happen on the active weights. beta: A float value, representing the beta value from the paper. Defaults to 0.0. **kwargs: Keyword arguments. Allowed to be one of `"clipnorm"` or `"clipvalue"`. `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips gradients by value. Reference: - [McMahan et al., 2013]( https://research.google.com/pubs/archive/41159.pdf) """ def __init__(self, learning_rate=0.001, learning_rate_power=-0.5, initial_accumulator_value=0.1, l1_regularization_strength=0.0, l2_regularization_strength=0.0, name='Ftrl', l2_shrinkage_regularization_strength=0.0, beta=0.0, **kwargs): super(Ftrl, self).__init__(name, **kwargs) if initial_accumulator_value < 0.0: raise ValueError( 'initial_accumulator_value %f needs to be positive or zero' % initial_accumulator_value) if learning_rate_power > 0.0: raise ValueError('learning_rate_power %f needs to be negative or zero' % learning_rate_power) if l1_regularization_strength < 0.0: raise ValueError( 'l1_regularization_strength %f needs to be positive or zero' % l1_regularization_strength) if l2_regularization_strength < 0.0: raise ValueError( 'l2_regularization_strength %f needs to be positive or zero' % l2_regularization_strength) if l2_shrinkage_regularization_strength < 0.0: raise ValueError( 'l2_shrinkage_regularization_strength %f needs to be positive' ' or zero' % l2_shrinkage_regularization_strength) self._set_hyper('learning_rate', learning_rate) self._set_hyper('decay', self._initial_decay) self._set_hyper('learning_rate_power', learning_rate_power) self._set_hyper('l1_regularization_strength', l1_regularization_strength) self._set_hyper('l2_regularization_strength', l2_regularization_strength) self._set_hyper('beta', beta) self._initial_accumulator_value = initial_accumulator_value self._l2_shrinkage_regularization_strength = ( l2_shrinkage_regularization_strength) def _create_slots(self, var_list): # Create the "accum" and "linear" slots. for var in var_list: dtype = var.dtype.base_dtype init = tf.compat.v1.constant_initializer( self._initial_accumulator_value, dtype=dtype) self.add_slot(var, 'accumulator', init) self.add_slot(var, 'linear') def _prepare_local(self, var_device, var_dtype, apply_state): super(Ftrl, self)._prepare_local(var_device, var_dtype, apply_state) apply_state[(var_device, var_dtype)].update( dict( learning_rate_power=tf.identity( self._get_hyper('learning_rate_power', var_dtype)), l1_regularization_strength=tf.identity( self._get_hyper('l1_regularization_strength', var_dtype)), l2_regularization_strength=tf.identity( self._get_hyper('l2_regularization_strength', var_dtype)), beta=tf.identity(self._get_hyper('beta', var_dtype)), l2_shrinkage_regularization_strength=tf.cast( self._l2_shrinkage_regularization_strength, var_dtype))) def _resource_apply_dense(self, grad, var, apply_state=None): var_device, var_dtype = var.device, var.dtype.base_dtype coefficients = ((apply_state or {}).get((var_device, var_dtype)) or self._fallback_apply_state(var_device, var_dtype)) # Adjust L2 regularization strength to include beta to avoid the underlying # TensorFlow ops needing to include it. adjusted_l2_regularization_strength = ( coefficients['l2_regularization_strength'] + coefficients['beta'] / (2. * coefficients['lr_t'])) accum = self.get_slot(var, 'accumulator') linear = self.get_slot(var, 'linear') if self._l2_shrinkage_regularization_strength <= 0.0: return tf.raw_ops.ResourceApplyFtrl( var=var.handle, accum=accum.handle, linear=linear.handle, grad=grad, lr=coefficients['lr_t'], l1=coefficients['l1_regularization_strength'], l2=adjusted_l2_regularization_strength, lr_power=coefficients['learning_rate_power'], use_locking=self._use_locking) else: return tf.raw_ops.ResourceApplyFtrlV2( var=var.handle, accum=accum.handle, linear=linear.handle, grad=grad, lr=coefficients['lr_t'], l1=coefficients['l1_regularization_strength'], l2=adjusted_l2_regularization_strength, l2_shrinkage=coefficients['l2_shrinkage_regularization_strength'], lr_power=coefficients['learning_rate_power'], use_locking=self._use_locking) def _resource_apply_sparse(self, grad, var, indices, apply_state=None): var_device, var_dtype = var.device, var.dtype.base_dtype coefficients = ((apply_state or {}).get((var_device, var_dtype)) or self._fallback_apply_state(var_device, var_dtype)) # Adjust L2 regularization strength to include beta to avoid the underlying # TensorFlow ops needing to include it. adjusted_l2_regularization_strength = ( coefficients['l2_regularization_strength'] + coefficients['beta'] / (2. * coefficients['lr_t'])) accum = self.get_slot(var, 'accumulator') linear = self.get_slot(var, 'linear') if self._l2_shrinkage_regularization_strength <= 0.0: return tf.raw_ops.ResourceSparseApplyFtrl( var=var.handle, accum=accum.handle, linear=linear.handle, grad=grad, indices=indices, lr=coefficients['lr_t'], l1=coefficients['l1_regularization_strength'], l2=adjusted_l2_regularization_strength, lr_power=coefficients['learning_rate_power'], use_locking=self._use_locking) else: return tf.raw_ops.ResourceSparseApplyFtrlV2( var=var.handle, accum=accum.handle, linear=linear.handle, grad=grad, indices=indices, lr=coefficients['lr_t'], l1=coefficients['l1_regularization_strength'], l2=adjusted_l2_regularization_strength, l2_shrinkage=coefficients['l2_shrinkage_regularization_strength'], lr_power=coefficients['learning_rate_power'], use_locking=self._use_locking) def get_config(self): config = super(Ftrl, self).get_config() config.update({ 'learning_rate': self._serialize_hyperparameter('learning_rate'), 'decay': self._initial_decay, 'initial_accumulator_value': self._initial_accumulator_value, 'learning_rate_power': self._serialize_hyperparameter('learning_rate_power'), 'l1_regularization_strength': self._serialize_hyperparameter('l1_regularization_strength'), 'l2_regularization_strength': self._serialize_hyperparameter('l2_regularization_strength'), 'beta': self._serialize_hyperparameter('beta'), 'l2_shrinkage_regularization_strength': self._l2_shrinkage_regularization_strength, }) return config
Ancestors
- OptimizerV2
- tensorflow.python.training.tracking.base.Trackable
Inherited members