text: # coding=utf-8
  # Copyright 2018 The Google AI Language Team Authors.
  #
  # 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.
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import re
  
  import tensorflow as tf
  
  
  def create_optimizer(loss, init_lr, num_train_steps, num_warmup_steps, use_tpu):
      """Creates an optimizer training op."""
      global_step = tf.compat.v1.train.get_or_create_global_step()
  
      learning_rate = tf.constant(value=init_lr, shape=[], dtype=tf.float32)
  
      # Implements linear decay of the learning rate.
      learning_rate = tf.compat.v1.train.polynomial_decay(
          learning_rate,
          global_step,
          num_train_steps,
          end_learning_rate=0.0,
          power=1.0,
          cycle=False)
  
      # Implements linear warmup. I.e., if global_step < num_warmup_steps, the
      # learning rate will be `global_step/num_warmup_steps * init_lr`.
      if num_warmup_steps:
          global_steps_int = tf.cast(global_step, tf.int32)
          warmup_steps_int = tf.constant(num_warmup_steps, dtype=tf.int32)
  
          global_steps_float = tf.cast(global_steps_int, tf.float32)
          warmup_steps_float = tf.cast(warmup_steps_int, tf.float32)
  
          warmup_percent_done = global_steps_float / warmup_steps_float
          warmup_learning_rate = init_lr * warmup_percent_done
  
          is_warmup = tf.cast(global_steps_int < warmup_steps_int, tf.float32)
          learning_rate = (
                  (1.0 - is_warmup) * learning_rate + is_warmup * warmup_learning_rate)
  
      # It is recommended that you use this optimizer for fine tuning, since this
      # is how the model was trained (note that the Adam m/v variables are NOT
      # loaded from init_checkpoint.)
      optimizer = AdamWeightDecayOptimizer(
          learning_rate=learning_rate,
          weight_decay_rate=0.01,
          beta_1=0.9,
          beta_2=0.999,
          epsilon=1e-6,
          exclude_from_weight_decay=["LayerNorm", "layer_norm", "bias"])
  
      if use_tpu:
          optimizer = tf.compat.v1.tpu.CrossShardOptimizer(optimizer)
  
      tvars = tf.compat.v1.trainable_variables()
      grads = tf.gradients(ys=loss, xs=tvars)
  
      # This is how the model was pre-trained.
      (grads, _) = tf.clip_by_global_norm(grads, clip_norm=1.0)
  
      train_op = optimizer.apply_gradients(
          zip(grads, tvars), global_step=global_step)
  
      new_global_step = global_step + 1
      train_op = tf.group(train_op, [global_step.assign(new_global_step)])
      return train_op
  
  
  class AdamWeightDecayOptimizer(tf.compat.v1.train.Optimizer):
      """A basic Adam optimizer that includes "correct" L2 weight decay."""
  
      def __init__(self,
                   learning_rate,
                   weight_decay_rate=0.0,
                   beta_1=0.9,
                   beta_2=0.999,
                   epsilon=1e-6,
                   exclude_from_weight_decay=None,
                   name="AdamWeightDecayOptimizer"):
          """Constructs a AdamWeightDecayOptimizer."""
          super(AdamWeightDecayOptimizer, self).__init__(False, name)
  
          self.learning_rate = learning_rate
          self.weight_decay_rate = weight_decay_rate
          self.beta_1 = beta_1
          self.beta_2 = beta_2
          self.epsilon = epsilon
          self.exclude_from_weight_decay = exclude_from_weight_decay
  
      def apply_gradients(self, grads_and_vars, global_step=None, name=None):
          """See base class."""
          assignments = []
          for (grad, param) in grads_and_vars:
              if grad is None or param is None:
                  continue
  
              param_name = self._get_variable_name(param.name)
  
              m = tf.compat.v1.get_variable(
                  name=param_name + "/adam_m",
                  shape=param.shape.as_list(),
                  dtype=tf.float32,
                  trainable=False,
                  initializer=tf.compat.v1.zeros_initializer())
              v = tf.compat.v1.get_variable(
                  name=param_name + "/adam_v",
                  shape=param.shape.as_list(),
                  dtype=tf.float32,
                  trainable=False,
                  initializer=tf.compat.v1.zeros_initializer())
  
              # Standard Adam update.
              next_m = (
                      tf.multiply(self.beta_1, m) + tf.multiply(1.0 - self.beta_1, grad))
              next_v = (
                      tf.multiply(self.beta_2, v) + tf.multiply(1.0 - self.beta_2,
                                                                tf.square(grad)))
  
              update = next_m / (tf.sqrt(next_v) + self.epsilon)
  
              # Just adding the square of the weights to the loss function is *not*
              # the correct way of using L2 regularization/weight decay with Adam,
              # since that will interact with the m and v parameters in strange ways.
              #
              # Instead we want ot decay the weights in a manner that doesn't interact
              # with the m/v parameters. This is equivalent to adding the square
              # of the weights to the loss with plain (non-momentum) SGD.
              if self._do_use_weight_decay(param_name):
                  update += self.weight_decay_rate * param
  
              update_with_lr = self.learning_rate * update
  
              next_param = param - update_with_lr
  
              assignments.extend(
                  [param.assign(next_param),
                   m.assign(next_m),
                   v.assign(next_v)])
          return tf.group(*assignments, name=name)
  
      def _do_use_weight_decay(self, param_name):
          """Whether to use L2 weight decay for `param_name`."""
          if not self.weight_decay_rate:
              return False
          if self.exclude_from_weight_decay:
              for r in self.exclude_from_weight_decay:
                  if re.search(r, param_name) is not None:
                      return False
          return True
  
      def _get_variable_name(self, param_name):
          """Get the variable name from the tensor name."""
          m = re.match("^(.*):\\d+$", param_name)
          if m is not None:
              param_name = m.group(1)
          return param_name
  