text: # Copyright (c) 2017-present, Facebook, Inc.
  # All rights reserved.
  #
  # This source code is licensed under the license found in the LICENSE file in
  # the root directory of this source tree. An additional grant of patent rights
  # can be found in the PATENTS file in the same directory.
  
  import math
  import torch
  import torch.optim
  
  from optimizer.base_optimizer import FairseqOptimizer
  
  
  class AdamOptimizer(FairseqOptimizer):
      def __init__(self, args, params):
          super().__init__(args, params)
          self._optimizer = Adam(params, **self.optimizer_config)
  
      @staticmethod
      def add_args(parser):
          """Add optimizer-specific arguments to the parser."""
          # fmt: off
          parser.add_argument('--adam-betas', default='(0.9, 0.999)', metavar='B',
                              help='betas for Adam optimizer')
          parser.add_argument('--adam-eps', type=float, default=1e-8, metavar='D',
                              help='epsilon for Adam optimizer')
          # fmt: on
  
      @property
      def optimizer_config(self):
          """
          Return a kwarg dictionary that will be used to override optimizer
          args stored in checkpoints. This allows us to load a checkpoint and
          resume training using a different set of optimizer args, e.g., with a
          different learning rate.
          """
          return {
              'lr': self.args.lr,
              'betas': eval(self.args.adam_betas),
              'eps': self.args.adam_eps,
              'weight_decay': self.args.weight_decay,
          }
  
  
  class Adam(torch.optim.Optimizer):
      """Implements Adam algorithm.
  
      This implementation is modified from torch.optimizer.Adam based on:
      `Fixed Weight Decay Regularization in Adam`
      (see https://arxiv.org/abs/1711.05101)
  
      It has been proposed in `Adam: A Method for Stochastic Optimization`_.
  
      Arguments:
          params (iterable): iterable of parameters to optimize or dicts defining
              parameter groups
          lr (float, optional): learning rate (default: 1e-3)
          betas (Tuple[float, float], optional): coefficients used for computing
              running averages of gradient and its square (default: (0.9, 0.999))
          eps (float, optional): term added to the denominator to improve
              numerical stability (default: 1e-8)
          weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
          amsgrad (boolean, optional): whether to use the AMSGrad variant of this
              algorithm from the paper `On the Convergence of Adam and Beyond`_
  
      .. _Adam\: A Method for Stochastic Optimization:
          https://arxiv.org/abs/1412.6980
      .. _On the Convergence of Adam and Beyond:
          https://openreview.net/forum?id=ryQu7f-RZ
      """
  
      def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                   weight_decay=0, amsgrad=False):
          defaults = dict(lr=lr, betas=betas, eps=eps,
                          weight_decay=weight_decay, amsgrad=amsgrad)
          super(Adam, self).__init__(params, defaults)
  
      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')
                  amsgrad = group['amsgrad']
  
                  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)
                      if amsgrad:
                          # Maintains max of all exp. moving avg. of sq. grad. values
                          state['max_exp_avg_sq'] = torch.zeros_like(p.data)
  
                  exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                  if amsgrad:
                      max_exp_avg_sq = state['max_exp_avg_sq']
                  beta1, beta2 = group['betas']
  
                  state['step'] += 1
  
                  # 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)
                  if amsgrad:
                      # Maintains the maximum of all 2nd moment running avg. till now
                      torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
                      # Use the max. for normalizing running avg. of gradient
                      denom = max_exp_avg_sq.sqrt().add_(group['eps'])
                  else:
                      denom = exp_avg_sq.sqrt().add_(group['eps'])
  
                  bias_correction1 = 1 - beta1 ** state['step']
                  bias_correction2 = 1 - beta2 ** state['step']
                  step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1
  
                  if group['weight_decay'] != 0:
                      p.data.add_(-group['weight_decay'] * group['lr'], p.data)
  
                  p.data.addcdiv_(-step_size, exp_avg, denom)
  
          return loss
  