# 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 from keras.optimizers.optimizer_v2 import optimizer_v2 # isort: off 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 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. 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().__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=" f"{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=" f"{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()._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"] / (2.0 * 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"] / (2.0 * 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().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, # noqa: E501 } ) return config