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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."""
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` needs to be positive or zero. Received: '
f'initial_accumulator_value={initial_accumulator_value}.')
if learning_rate_power > 0.0:
raise ValueError(
'`learning_rate_power` needs to be negative or zero. Received: '
f'learning_rate_power={learning_rate_power}.')
if l1_regularization_strength < 0.0:
raise ValueError(
'`l1_regularization_strength` needs to be positive or zero. '
f'Received: l1_regularization_strength={l1_regularization_strength}.')
if l2_regularization_strength < 0.0:
raise ValueError(
'`l2_regularization_strength` needs to be positive or zero. '
f'Received: l2_regularization_strength={l2_regularization_strength}.')
if l2_shrinkage_regularization_strength < 0.0:
raise ValueError(
'`l2_shrinkage_regularization_strength` needs to be positive or '
'zero. Received: l2_shrinkage_regularization_strength'
f'={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