# Copyright 2022 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 optimizer implementation.""" import tensorflow.compat.v2 as tf from keras.optimizers.optimizer_experimental import optimizer from keras.utils import generic_utils # isort: off from tensorflow.python.util.tf_export import keras_export @generic_utils.register_keras_serializable() @keras_export("keras.optimizers.experimental.Ftrl", v1=[]) class Ftrl(optimizer.Optimizer): 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 = (n ** -lr_power - prev_n ** -lr_power) / 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 - `lr_power` is the power to scale n. 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, a schedule that is a `tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable that takes no arguments and returns the actual value to use. The learning rate. Defaults to 0.001. 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. 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. {{base_optimizer_keyword_args}} """ 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, l2_shrinkage_regularization_strength=0.0, beta=0.0, clipnorm=None, clipvalue=None, global_clipnorm=None, use_ema=False, ema_momentum=0.99, ema_overwrite_frequency=None, jit_compile=True, name="Ftrl", **kwargs, ): super().__init__( name=name, clipnorm=clipnorm, clipvalue=clipvalue, global_clipnorm=global_clipnorm, use_ema=use_ema, ema_momentum=ema_momentum, ema_overwrite_frequency=ema_overwrite_frequency, jit_compile=jit_compile, **kwargs, ) if initial_accumulator_value < 0.0: raise ValueError( "`initial_accumulator_value` needs to be positive or zero. " f"Received: initial_accumulator_value=" f"{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._learning_rate = self._build_learning_rate(learning_rate) self.learning_rate_power = learning_rate_power self.initial_accumulator_value = initial_accumulator_value self.l1_regularization_strength = l1_regularization_strength self.l2_regularization_strength = l2_regularization_strength self.l2_shrinkage_regularization_strength = ( l2_shrinkage_regularization_strength ) self.beta = beta def build(self, var_list): """Initialize optimizer variables. Args: var_list: list of model variables to build Ftrl variables on. """ super().build(var_list) if hasattr(self, "_built") and self._built: return self._accumulators = [] self._linears = [] for var in var_list: self._accumulators.append( self.add_variable_from_reference( model_variable=var, variable_name="accumulator", initial_value=tf.cast( tf.fill( dims=var.shape, value=self.initial_accumulator_value ), dtype=var.dtype, ), ) ) self._linears.append( self.add_variable_from_reference( model_variable=var, variable_name="linear" ) ) self._built = True def update_step(self, gradient, variable): """Update step given gradient and the associated model variable.""" lr = tf.cast(self.learning_rate, variable.dtype) var_key = self._var_key(variable) accum = self._accumulators[self._index_dict[var_key]] linear = self._linears[self._index_dict[var_key]] lr_power = self.learning_rate_power l2_reg = self.l2_regularization_strength l2_reg = l2_reg + self.beta / (2.0 * lr) # Ftrl optimizer has the same implementation for sparse and dense # gradients update. grad_to_use = ( gradient + 2 * self.l2_shrinkage_regularization_strength * variable ) new_accum = accum + tf.pow(gradient, 2) linear.assign_add( grad_to_use - (tf.pow(new_accum, -lr_power) - tf.pow(accum, -lr_power)) / lr * variable ) quadratic = tf.pow(new_accum, (-lr_power)) / lr + 2 * l2_reg linear_clipped = tf.clip_by_value( linear, -self.l1_regularization_strength, self.l1_regularization_strength, ) variable.assign((linear_clipped - linear) / quadratic) accum.assign(new_accum) def get_config(self): config = super().get_config() config.update( { "learning_rate": self._serialize_hyperparameter( self._learning_rate ), "learning_rate_power": self.learning_rate_power, "initial_accumulator_value": self.initial_accumulator_value, "l1_regularization_strength": self.l1_regularization_strength, "l2_regularization_strength": self.l2_regularization_strength, "l2_shrinkage_regularization_strength": self.l2_shrinkage_regularization_strength, # noqa: E501 "beta": self.beta, } ) return config Ftrl.__doc__ = Ftrl.__doc__.replace( "{{base_optimizer_keyword_args}}", optimizer.base_optimizer_keyword_args )