text: import math
  import torch
  
  from torch.optim.optimizer import Optimizer
  
  
  class RAdam(Optimizer):
      """Rectified Adam optimizer."""
  
      def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, weight_decay=0):
          """Initilize RAdam optimizer."""
          defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay)
          self.buffer = [[None, None, None] for ind in range(10)]
          super(RAdam, self).__init__(params, defaults)
  
      def __setstate__(self, state):
          """Set state."""
          super(RAdam, self).__setstate__(state)
  
      def step(self, closure=None):
          """Run one step."""
          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.float()
                  if grad.is_sparse:
                      raise RuntimeError('RAdam does not support sparse gradients')
  
                  p_data_fp32 = p.data.float()
  
                  state = self.state[p]
  
                  if len(state) == 0:
                      state['step'] = 0
                      state['exp_avg'] = torch.zeros_like(p_data_fp32)
                      state['exp_avg_sq'] = torch.zeros_like(p_data_fp32)
                  else:
                      state['exp_avg'] = state['exp_avg'].type_as(p_data_fp32)
                      state['exp_avg_sq'] = state['exp_avg_sq'].type_as(p_data_fp32)
  
                  exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                  beta1, beta2 = group['betas']
  
                  exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
                  exp_avg.mul_(beta1).add_(1 - beta1, grad)
  
                  state['step'] += 1
                  buffered = self.buffer[int(state['step'] % 10)]
                  if state['step'] == buffered[0]:
                      N_sma, step_size = buffered[1], buffered[2]
                  else:
                      buffered[0] = state['step']
                      beta2_t = beta2 ** state['step']
                      N_sma_max = 2 / (1 - beta2) - 1
                      N_sma = N_sma_max - 2 * state['step'] * beta2_t / (1 - beta2_t)
                      buffered[1] = N_sma
  
                      # more conservative since it's an approximated value
                      if N_sma >= 5:
                          step_size = math.sqrt(
                              (1 - beta2_t) * (N_sma - 4) / (N_sma_max - 4) * (N_sma - 2) / N_sma * N_sma_max / (N_sma_max - 2)) / (1 - beta1 ** state['step'])  # NOQA
                      else:
                          step_size = 1.0 / (1 - beta1 ** state['step'])
                      buffered[2] = step_size
  
                  if group['weight_decay'] != 0:
                      p_data_fp32.add_(-group['weight_decay'] * group['lr'], p_data_fp32)
  
                  # more conservative since it's an approximated value
                  if N_sma >= 5:
                      denom = exp_avg_sq.sqrt().add_(group['eps'])
                      p_data_fp32.addcdiv_(-step_size * group['lr'], exp_avg, denom)
                  else:
                      p_data_fp32.add_(-step_size * group['lr'], exp_avg)
  
                  p.data.copy_(p_data_fp32)
  
          return loss
  