class_docstr: Implements AdamP algorithm.
  
  It has been proposed in `Slowing Down the Weight Norm Increase in
  Momentum-based Optimizers`__
  
  Arguments:
      params: iterable of parameters to optimize or dicts defining
          parameter groups
      lr: learning rate (default: 1e-3)
      betas: coefficients used for computing
          running averages of gradient and its square (default: (0.9, 0.999))
      eps: term added to the denominator to improve
          numerical stability (default: 1e-8)
      weight_decay: weight decay (L2 penalty) (default: 0)
      delta: threhold that determines whether a set of parameters is scale
          invariant or not (default: 0.1)
      wd_ratio: relative weight decay applied on scale-invariant parameters
          compared to that applied on scale-variant parameters (default: 0.1)
      nesterov: enables Nesterov momentum (default: False)
  
  
  Example:
      >>> import torch_optimizer as optim
      >>> optimizer = optim.AdamP(model.parameters(), lr=0.1)
      >>> optimizer.zero_grad()
      >>> loss_fn(model(input), target).backward()
      >>> optimizer.step()
  
   __ https://arxiv.org/abs/2006.08217
  
  Note:
      Reference code: https://github.com/clovaai/AdamP
docstr: Performs a single optimization step.
  
  Arguments:
      closure: A closure that reevaluates the model and returns the loss.
code: def step(self, closure: OptLossClosure = None) -> OptFloat:
      r"""Performs a single optimization step.
  
      Arguments:
          closure: 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
              beta1, beta2 = group["betas"]
              nesterov = group["nesterov"]
  
              state = self.state[p]
  
              # State initialization
              if len(state) == 0:
                  state["step"] = 0
                  state["exp_avg"] = torch.zeros_like(
                      p.data, memory_format=torch.preserve_format
                  )
                  state["exp_avg_sq"] = torch.zeros_like(
                      p.data, memory_format=torch.preserve_format
                  )
  
              # Adam
              exp_avg, exp_avg_sq = (
                  state["exp_avg"],
                  state["exp_avg_sq"],
              )
  
              state["step"] += 1
              bias_correction1 = 1 - beta1 ** state["step"]
              bias_correction2 = 1 - beta2 ** state["step"]
  
              exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
              exp_avg_sq.mul_(beta2).addcmul_(
                  grad, grad, value=1 - beta2
              )
  
              denom = (
                  exp_avg_sq.sqrt() / math.sqrt(bias_correction2)
              ).add_(group["eps"])
              step_size = group["lr"] / bias_correction1
  
              if nesterov:
                  perturb = (
                      beta1 * exp_avg + (1 - beta1) * grad
                  ) / denom
              else:
                  perturb = exp_avg / denom
  
              # Projection
              wd_ratio = 1
              if len(p.shape) > 1:
                  perturb, wd_ratio = self._projection(
                      p,
                      grad,
                      perturb,
                      group["delta"],
                      group["wd_ratio"],
                      group["eps"],
                  )
  
              # Weight decay
              if group["weight_decay"] > 0:
                  p.data.mul_(
                      1 - group["lr"] * group["weight_decay"] * wd_ratio
                  )
  
              # Step
              p.data.add_(perturb, alpha=-step_size)
  
      return loss
  
file_path: pytorch-optimizer/torch_optimizer/adamp.py
imports: import math
  import torch
  from torch.optim.optimizer import Optimizer
  from .types import Betas2, OptFloat, OptLossClosure, Params
label_desc: Use image node_id 6 for calling the AdamP obj's underlying member method code with example usage: obj.step(closure) and returns: loss