text: import torch
  from torch.optim.optimizer import Optimizer
  from collections import defaultdict
  
  
  class Lookahead(Optimizer):
      """
      PyTorch implementation of the lookahead wrapper.
      Lookahead Optimizer: https://arxiv.org/abs/1907.08610
  
      We found that evaluation performance is typically better using the slow weights.
      This can be done in PyTorch with something like this in your eval loop:
      if args.lookahead:
          optimizer._backup_and_load_cache()
          val_loss = eval_func(model)
          optimizer._clear_and_load_backup()
      """
      def __init__(self, optimizer, default: dict = None, params=None, alpha=0.5, k=6, pullback_momentum="none"):
          """
          :param optimizer:inner optimizer
          :param k (int): number of lookahead steps
          :param alpha(float): linear interpolation factor. 1.0 recovers the inner optimizer.
          :param pullback_momentum (str): change to inner optimizer momentum on interpolation update
          """
          super().__init__(params, default)
          if not 0.0 <= alpha <= 1.0:
              raise ValueError(f'Invalid slow update rate: {alpha}')
          if not 1 <= k:
              raise ValueError(f'Invalid lookahead steps: {k}')
          self.optimizer = optimizer
          self.param_groups = self.optimizer.param_groups if not params else params
          self.alpha = alpha
          self.k = k
          self.step_counter = 0
          assert pullback_momentum in ["reset", "pullback", "none"]
          self.pullback_momentum = pullback_momentum
          self.state = defaultdict(dict)
  
          # Cache the current optimizer parameters
          for group in self.optimizer.param_groups:
              for p in group['params']:
                  param_state = self.state[p]
                  param_state['cached_params'] = torch.zeros_like(p.data)
                  param_state['cached_params'].copy_(p.data)
  
      def __getstate__(self):
          return {
              'state': self.state,
              'optimizer': self.optimizer,
              'alpha': self.alpha,
              'step_counter': self.step_counter,
              'k': self.k,
              'pullback_momentum': self.pullback_momentum
          }
  
      def zero_grad(self, **kwargs):
          self.optimizer.zero_grad()
  
      def state_dict(self):
          return self.optimizer.state_dict()
  
      def load_state_dict(self, state_dict):
          self.optimizer.load_state_dict(state_dict)
  
      def _backup_and_load_cache(self):
          """Useful for performing evaluation on the slow weights (which typically generalize better)
          """
          for group in self.optimizer.param_groups:
              for p in group['params']:
                  param_state = self.state[p]
                  param_state['backup_params'] = torch.zeros_like(p.data)
                  param_state['backup_params'].copy_(p.data)
                  p.data.copy_(param_state['cached_params'])
  
      def _clear_and_load_backup(self):
          for group in self.optimizer.param_groups:
              for p in group['params']:
                  param_state = self.state[p]
                  p.data.copy_(param_state['backup_params'])
                  del param_state['backup_params']
  
      def step(self, closure=None):
          """Performs a single Lookahead optimization step.
          Arguments:
              closure (callable, optional): A closure that reevaluates the model
                  and returns the loss.
          """
          loss = self.optimizer.step(closure)
          self.step_counter += 1
  
          if self.step_counter >= self.k:
              self.step_counter = 0
              # Lookahead and cache the current optimizer parameters
              for group in self.optimizer.param_groups:
                  for p in group['params']:
                      param_state = self.state[p]
                      p.data.mul_(self.alpha).add_(1.0 - self.alpha, param_state['cached_params'])  # crucial line
                      param_state['cached_params'].copy_(p.data)
                      if self.pullback_momentum == "pullback":
                          internal_momentum = self.optimizer.state[p]["momentum_buffer"]
                          self.optimizer.state[p]["momentum_buffer"] = internal_momentum.mul_(self.alpha).add_(
                              1.0 - self.alpha, param_state["cached_mom"])
                          param_state["cached_mom"] = self.optimizer.state[p]["momentum_buffer"]
                      elif self.pullback_momentum == "reset":
                          self.optimizer.state[p]["momentum_buffer"] = torch.zeros_like(p.data)
  
          return loss
  