content: # coding=utf-8
  # Copyright 2018 The Open AI Team Authors and The HuggingFace Inc. team.
  #
  # 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.
  """PyTorch optimization for OpenAI GPT model."""
  
  import math
  import torch
  from torch.optim import Optimizer
  from torch.optim.optimizer import required
  from torch.nn.utils import clip_grad_norm_
  import logging
  from .optimization import SCHEDULES, _LRSchedule, WarmupCosineWithWarmupRestartsSchedule, \
      WarmupCosineWithHardRestartsSchedule, WarmupCosineSchedule, WarmupLinearSchedule, WarmupConstantSchedule
  
  logger = logging.getLogger(__name__)
  
  
  class OpenAIAdam(Optimizer):
      """Implements Open AI version of Adam algorithm with weight decay fix.
      """
      def __init__(self, params, lr=required, schedule='warmup_linear', warmup=-1, t_total=-1,
                   b1=0.9, b2=0.999, e=1e-8, weight_decay=0,
                   vector_l2=False, max_grad_norm=-1, **kwargs):
          if lr is not required and lr < 0.0:
              raise ValueError("Invalid learning rate: {} - should be >= 0.0".format(lr))
          if not isinstance(schedule, _LRSchedule) and schedule not in SCHEDULES:
              raise ValueError("Invalid schedule parameter: {}".format(schedule))
          if not 0.0 <= b1 < 1.0:
              raise ValueError("Invalid b1 parameter: {} - should be in [0.0, 1.0[".format(b1))
          if not 0.0 <= b2 < 1.0:
              raise ValueError("Invalid b2 parameter: {} - should be in [0.0, 1.0[".format(b2))
          if not e >= 0.0:
              raise ValueError("Invalid epsilon value: {} - should be >= 0.0".format(e))
          # initialize schedule object
          if not isinstance(schedule, _LRSchedule):
              schedule_type = SCHEDULES[schedule]
              schedule = schedule_type(warmup=warmup, t_total=t_total)
          else:
              if warmup != -1 or t_total != -1:
                  logger.warning("warmup and t_total on the optimizer are ineffective when _LRSchedule object is provided as schedule. "
                                 "Please specify custom warmup and t_total in _LRSchedule object.")
          defaults = dict(lr=lr, schedule=schedule,
                          b1=b1, b2=b2, e=e, weight_decay=weight_decay, vector_l2=vector_l2,
                          max_grad_norm=max_grad_norm)
          super(OpenAIAdam, self).__init__(params, defaults)
  
      def get_lr(self):
          lr = []
          for group in self.param_groups:
              for p in group['params']:
                  state = self.state[p]
                  if len(state) == 0:
                      return [0]
                  lr_scheduled = group['lr']
                  lr_scheduled *= group['schedule'].get_lr(state['step'])
                  lr.append(lr_scheduled)
          return lr
  
      def step(self, closure=None):
          """Performs a single optimization step.
  
          Arguments:
              closure (callable, optional): A closure that reevaluates the model
                  and returns the loss.
          """
          loss = None
          if closure is not None:
              loss = closure()
  
          for group in self.param_groups:
              for p in group['params']:
                  if p.grad is None:
                      continue
                  grad = p.grad.data
                  if grad.is_sparse:
                      raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
  
                  state = self.state[p]
  
                  # State initialization
                  if len(state) == 0:
                      state['step'] = 0
                      # Exponential moving average of gradient values
                      state['exp_avg'] = torch.zeros_like(p.data)
                      # Exponential moving average of squared gradient values
                      state['exp_avg_sq'] = torch.zeros_like(p.data)
  
                  exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                  beta1, beta2 = group['b1'], group['b2']
  
                  state['step'] += 1
  
                  # Add grad clipping
                  if group['max_grad_norm'] > 0:
                      clip_grad_norm_(p, group['max_grad_norm'])
  
                  # Decay the first and second moment running average coefficient
                  exp_avg.mul_(beta1).add_(1 - beta1, grad)
                  exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
                  denom = exp_avg_sq.sqrt().add_(group['e'])
  
                  bias_correction1 = 1 - beta1 ** state['step']
                  bias_correction2 = 1 - beta2 ** state['step']
  
                  lr_scheduled = group['lr']
                  lr_scheduled *= group['schedule'].get_lr(state['step'])
  
                  step_size = lr_scheduled * math.sqrt(bias_correction2) / bias_correction1
  
                  p.data.addcdiv_(-step_size, exp_avg, denom)
  
                  # Add weight decay at the end (fixed version)
                  if (len(p.size()) > 1 or group['vector_l2']) and group['weight_decay'] > 0:
                      p.data.add_(-lr_scheduled * group['weight_decay'], p.data)
  
          return loss
  