text: """ Borrowed from https://github.com/dgriff777/rl_a3c_pytorch. """
  
  from __future__ import division
  
  import math
  from collections import defaultdict
  
  import torch
  import torch.optim as optim
  
  
  class SharedAdam(optim.Optimizer):
      """Implements Adam algorithm with shared states.
      """
  
      def __init__(self,
                   params,
                   lr=1e-3,
                   betas=(0.9, 0.999),
                   eps=1e-3,
                   weight_decay=0,
                   amsgrad=True):
          # TODO: remove constants
          defaults = defaultdict(
              lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, amsgrad=amsgrad
          )
          super(SharedAdam, self).__init__(params, defaults)
  
          for group in self.param_groups:
              for p in group["params"]:
                  if p.requires_grad:
                      state = self.state[p]
                      state["step"] = torch.zeros(1)
                      state["exp_avg"] = p.data.new().resize_as_(p.data).zero_()
                      state["exp_avg_sq"] = p.data.new().resize_as_(p.data).zero_()
                      state["max_exp_avg_sq"] = p.data.new().resize_as_(p.data).zero_()
  
          print("initialized optimizer.")
  
      def share_memory(self):
          print("attempting to share memory.")
          try:
              for group in self.param_groups:
                  for p in group["params"]:
                      state = self.state[p]
                      state["step"].share_memory_()
                      state["exp_avg"].share_memory_()
                      state["exp_avg_sq"].share_memory_()
                      state["max_exp_avg_sq"].share_memory_()
          except Exception as e:
              print(e)
          print("sharing memory.")
  
      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]
  
                  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
  
                  if group["weight_decay"] != 0:
                      grad = grad.add(group["weight_decay"], p.data)
  
                  # 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"].item()
                  bias_correction2 = 1 - beta2 ** state["step"].item()
                  step_size = group["lr"] * math.sqrt(bias_correction2) / bias_correction1
  
                  p.data.addcdiv_(-step_size, exp_avg, denom)
  
          return loss
  