Python Programming

Recap

So far we saw how to use the backward() method to compute the gradient automatically. For instance, the code below evaluates the gradient of the loss function $L(\theta) = \theta^2$ at the value $\theta_0 = 1$.

import torch

tensor_0 = torch.Tensor([1])
theta = torch.nn.Parameter(tensor_0)

loss = theta * theta
print(theta.grad)
loss.backward()
print(theta.grad)

None
tensor([2.])

So, now we have the gradient $\dfrac{\partial L}{\partial \theta}$ automatically computed.

But…

But we still have to perform gradient descent manually!

$\theta \leftarrow \theta - \lambda \dfrac{\partial L}{\partial \theta}$

If we try to print $\theta$ after running the code above, we can see that its value has not changed since its initialisation:

print(theta)

Parameter containing:
tensor([1.], requires_grad=True)

So this means that $\theta$ has not yet been updated.

What we would like to have: automatic gradient descent!

Given that we have $\dfrac{\partial L}{\partial \theta}(\theta)$ automatically computed, can we also have $\theta$ updated to minimise the loss using gradient descent?

$\theta \leftarrow \theta - \lambda \dfrac{\partial L}{\partial \theta}$