class_docstr: Implements stochastic gradient descent (optionally with momentum).
  Nesterov momentum is based on the formula from
  `On the importance of initialization and momentum in deep learning`__.
  Args:
      params (iterable): iterable of parameters to optimize or dicts defining
          parameter groups
      lr (float): learning rate
      momentum (float, optional): momentum factor (default: 0)
      weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
      dampening (float, optional): dampening for momentum (default: 0)
      nesterov (bool, optional): enables Nesterov momentum (default: False)
      grad_threshold (float, optional): imposes a threshold on the magnitude of gradient values.
          Gradient values with magnitude above the threshold will be replaced with 0.
  Example:
      >>> optimizer = torch.optim.SGD(model.parameters(), lr=0.1, momentum=0.9)
      >>> optimizer.zero_grad()
      >>> loss_fn(model(input), target).backward()
      >>> optimizer.step()
  __ http://www.cs.toronto.edu/%7Ehinton/absps/momentum.pdf
  .. note::
      The implementation of SGD with Momentum/Nesterov subtly differs from
      Sutskever et. al. and implementations in some other frameworks.
      Considering the specific case of Momentum, the update can be written as
      .. math::
          \begin{aligned}
              v_{t+1} & = \mu * v_{t} + g_{t+1}, \\
              p_{t+1} & = p_{t} - \text{lr} * v_{t+1},
          \end{aligned}
      where :math:`p`, :math:`g`, :math:`v` and :math:`\mu` denote the
      parameters, gradient, velocity, and momentum respectively.
      This is in contrast to Sutskever et. al. and
      other frameworks which employ an update of the form
      .. math::
          \begin{aligned}
              v_{t+1} & = \mu * v_{t} + \text{lr} * g_{t+1}, \\
              p_{t+1} & = p_{t} - v_{t+1}.
          \end{aligned}
      The Nesterov version is analogously modified.
docstr: Performs a single optimization step.
  Arguments:
      closure (callable, optional): A closure that reevaluates the model
          and returns the loss.
docstr_tok: ["Performs","a","single","optimization","step",".","Arguments",":","closure","(","callable",",","optional",")",":","A","closure","that","reevaluates","the","model","and","returns","the","loss","."]
code: def step(self, closure=None):
      """Performs a single optimization step.
      Arguments:
          closure (callable, optional): A closure that reevaluates the model
              and returns the loss.
      """
      with crypten.no_grad():
          loss = None
          if closure is not None:
              with crypten.enable_grad():
                  loss = closure()
  
          for group in self.param_groups:
              weight_decay = group["weight_decay"]
              momentum = group["momentum"]
              dampening = group["dampening"]
              nesterov = group["nesterov"]
  
              for p in group["params"]:
                  if p.grad is None:
                      continue
  
                  # Threshold gradients to prevent gradient explosion
                  if self.square_threshold is not None:
                      d_p = p.grad.mul(
                          p.grad.square().lt(self.square_threshold)
                      )
                  else:
                      d_p = p.grad
  
                  if weight_decay != 0:
                      d_p = d_p.add(p.mul(weight_decay))
                  if momentum != 0:
                      param_state = self.state[id(p)]
                      if "momentum_buffer" not in param_state:
                          buf = param_state[
                              "momentum_buffer"
                          ] = d_p.clone().detach()
                      else:
                          buf = param_state["momentum_buffer"]
                          buf.mul_(momentum).add_(
                              d_p.mul(1 - dampening)
                          )
                      if nesterov:
                          d_p = d_p.add(buf.mul(momentum))
                      else:
                          d_p = buf
  
                  p.sub_(d_p.mul(group["lr"]))
  
          return loss
  
imports: import crypten
  from .optimizer import Optimizer
label_desc: Use image node_id 3 for calling the SGD obj's underlying member method code with example usage: obj.step(closure) and returns: loss