RMSPROP

def rmsprop_update(loss, params, grad_sq, lr=1e-3, alpha=0.8, epsilon=1e-8):
  """
  Perform an RMSprop update on a collection of parameters
  Args:
    loss: Tensor
      A scalar tensor containing the loss whose gradient will be computed
    params: Iterable
      Collection of parameters with respect to which we compute gradients
    grad_sq: Iterable
      Moving average of squared gradients
    lr: Float
      Scalar specifying the learning rate or step-size for the update
    alpha: Float
      Moving average parameter
    epsilon: Float
      quotient for numerical stability
  Returns:
    Nothing
  """
  # Clear up gradients as Pytorch automatically accumulates gradients from
  # successive backward calls
  zero_grad(params)
  # Compute gradients on given objective
  loss.backward()

  with torch.no_grad():
    for (par, gsq) in zip(params, grad_sq):
      # Update estimate of gradient variance
      gsq.data = alpha * gsq.data + (1 - alpha) * par.grad**2
      # Update parameters
      par.data -=  lr * (par.grad / (epsilon + gsq.data)**0.5)