Nesterov Accelerated Gradient Descent A variant of Stochastic Gradient Descent also considers the penultimate update to include more statistics for optimization: 𝜃̃ =𝜃+𝑣old⋅𝑚𝑡𝑚 𝑣=𝑣old⋅𝑚𝑡𝑚+𝜂⋅(−∂𝐿(𝜃̃ )∂𝜃) 𝜃=𝜃̃ Help me complete the following code based on the above question class NAGD(Optimizer): def __init__(self, params, lr=0.2, momentum=0.9) -> None: super().__init__(params, {'lr': lr, 'momentum': momentum}) self.lr = lr # maybe you need some more code here def step(self): with torch.no_grad(): for i, p in enumerate(self.param_groups[0]['params']): if p.grad is not None: # update parameters ...

Here is the completed code for Nesterov Accelerated Gradient Descent:

class NAGD(Optimizer):
    def __init__(self, params, lr=0.2, momentum=0.9) -> None:
        super().__init__(params, {'lr': lr, 'momentum': momentum})
        self.lr = lr
        self.momentum = momentum
        self.v = {}  # initialize velocity as an empty dictionary
        for param in self.param_groups[0]['params']:
            self.v[param] = torch.zeros_like(param.data)  # initialize velocity for each parameter as a tensor of zeros

    def step(self):
        with torch.no_grad():
            for i, p in enumerate(self.param_groups[0]['params']):
                if p.grad is not None:
                    # update velocity
                    self.v[p] = self.momentum * self.v[p] + self.lr * (-p.grad)
                    # compute Nesterov update
                    p_nesterov = p.data - self.momentum * self.v[p]
                    # update parameters
                    p.data.copy_(p_nesterov)

In the above code, we initialize the velocity `self.v` for each parameter as a tensor of zeros in the constructor. Then, in the `step()` method, we first update the velocity using the gradient of the current parameter value. Next, we compute the Nesterov update by subtracting the momentum-scaled velocity from the current parameter value. Finally, we update the parameter with the Nesterov update.