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 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

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). If None, 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. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_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