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# 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."""
# pylint: disable=g-classes-have-attributes
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.keras.optimizer_v2 import optimizer_v2
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import init_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.training import gen_training_ops
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.
See Algorithm 1 of this
[paper](https://research.google.com/pubs/archive/41159.pdf).
This version has support for both online L2 (the L2 penalty given in the paper
above) and shrinkage-type L2 (which is the addition of an L2 penalty to the
loss function).
Initialization:
$$t = 0$$
$$n_{0} = 0$$
$$\sigma_{0} = 0$$
$$z_{0} = 0$$
Update ($$i$$ is variable index, $$\alpha$$ is the learning rate):
$$t = t + 1$$
$$n_{t,i} = n_{t-1,i} + g_{t,i}^{2}$$
$$\sigma_{t,i} = (\sqrt{n_{t,i}} - \sqrt{n_{t-1,i}}) / \alpha$$
$$z_{t,i} = z_{t-1,i} + g_{t,i} - \sigma_{t,i} * w_{t,i}$$
$$w_{t,i} =\begin{cases} 0 & | z_{i}| \leqslant \lambda _{1} ,\\
\ -\left(\frac{\beta +\sqrt{n_{t,i}}}{\alpha }
+\lambda _{2}\right)^{-1}( z_{i} -sgn(z_{i} )
*\lambda _{1}) & otherwise.\end{cases}$$
Check the documentation for the l2_shrinkage_regularization_strength
parameter for more details when shrinkage is enabled, in which case gradient
is replaced with 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:
- [paper](
https://www.eecs.tufts.edu/~dsculley/papers/ad-click-prediction.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 = init_ops.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=array_ops.identity(
self._get_hyper('learning_rate_power', var_dtype)),
l1_regularization_strength=array_ops.identity(
self._get_hyper('l1_regularization_strength', var_dtype)),
l2_regularization_strength=array_ops.identity(
self._get_hyper('l2_regularization_strength', var_dtype)),
beta=array_ops.identity(self._get_hyper('beta', var_dtype)),
l2_shrinkage_regularization_strength=math_ops.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 gen_training_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 gen_training_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 gen_training_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 gen_training_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