class_docstr: Implements Novograd optimization algorithm.
  
  It has been proposed in `Stochastic Gradient Methods with Layer-wise
  Adaptive Moments for Training of Deep Networks`__.
  
  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: (0.95, 0))
      eps: term added to the denominator to improve
          numerical stability (default: 1e-8)
      weight_decay: weight decay (L2 penalty) (default: 0)
      grad_averaging: gradient averaging (default: False)
      amsgrad: whether to use the AMSGrad variant of this
          algorithm from the paper `On the Convergence of Adam and Beyond`
          (default: False)
  
  Example:
      >>> import torch_optimizer as optim
      >>> optimizer = optim.Yogi(model.parameters(), lr=0.1)
      >>> optimizer.zero_grad()
      >>> loss_fn(model(input), target).backward()
      >>> scheduler = StepLR(optimizer, step_size=1, gamma=0.7)
      >>> optimizer.step()
      >>> scheduler.step()
  
  __ https://arxiv.org/abs/1905.11286
  
  Note:
      Reference code: https://github.com/NVIDIA/DeepLearningExamples
docstr: Performs a single optimization step.
  
  Arguments:
      closure: A closure that reevaluates the model and returns the loss.
docstr_tok: ["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
              if grad.is_sparse:
                  msg = (
                      "NovoGrad does not support sparse gradients, "
                      "please consider SparseAdam instead"
                  )
                  raise RuntimeError(msg)
              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, memory_format=torch.preserve_format
                  )
                  # Exponential moving average of squared gradient values
                  state["exp_avg_sq"] = torch.zeros([]).to(
                      state["exp_avg"].device
                  )
                  if amsgrad:
                      # Maintains max of all exp. moving avg. of sq.
                      # grad. values
                      state["max_exp_avg_sq"] = torch.zeros([]).to(
                          state["exp_avg"].device
                      )
  
              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
  
              norm = torch.sum(torch.pow(grad, 2))
  
              if exp_avg_sq == 0:
                  exp_avg_sq.copy_(norm)
              else:
                  exp_avg_sq.mul_(beta2).add_(norm, alpha=1 - beta2)
  
              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"])
  
              grad.div_(denom)
              if group["weight_decay"] != 0:
                  grad.add_(p.data, alpha=group["weight_decay"])
              if group["grad_averaging"]:
                  grad.mul_(1 - beta1)
              exp_avg.mul_(beta1).add_(grad)
  
              p.data.add_(exp_avg, alpha=-group["lr"])
  
      return loss
  
imports: import torch
  from torch.optim.optimizer import Optimizer
  from .types import Betas2, OptFloat, OptLossClosure, Params
label_desc: Use image node_id 3 for calling the NovoGrad obj's underlying member method code with example usage: obj.step(closure) and returns: loss