text: from torch.optim import Optimizer
  import torch
  import math
  
  
  class PadamStar(Optimizer):
      """Implements Partially adaptive momentum estimation (Padam) algorithm.
          params (iterable): iterable of parameters to optimize or dicts defining
              parameter groups
          lr (float, optional): learning rate (default: 1e-1)
          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)
          partial (float, optional): partially adaptive parameter
      """
  
      def __init__(self, params, lr=1e-1, betas=(0.9, 0.999), eps=1e-8, weight_decay=0, amsgrad=True, gamma=0):
          if not 0.0 <= betas[0] < 1.0:
              raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
          if not 0.0 <= betas[1] < 1.0:
              raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
          defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay, amsgrad=amsgrad, gamma = gamma)
          super(PadamStar, 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)
  
                      state['B_old'] = 0
                      state['B_new'] = 1
  
                      state['be_sgd'] = False
  
                      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
  
                  if group['weight_decay'] != 0:
                      grad = grad.add(group['weight_decay'], p.data)
  
                  if not state['be_sgd']:
                      partial = 0.5 * (1 - state['B_old'] / state['B_new'])
                      state['B_old'] += math.pow(state['step'], -group['gamma'])
                      state['B_new'] += math.pow(state['step'] + 1, -group['gamma'])
                      if partial <= 1e-6:
                          state['be_sgd'] = True
                  else:
                      partial = 0
  
                  # 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
  
                  p.data.addcdiv_(-step_size, exp_avg, denom ** (partial * 2))
  
          return loss