I want different losses to have their gradients computed with respect to different variables, and those variables to then all step together.
Here’s a simple example demonstrating what I want:
import torch as T
x = T.randn(3, requires_grad = True)
y = T.randn(4, requires_grad = True)
z = T.randn(5, requires_grad = True)

x_opt = T.optim.Adadelta([x])
y_opt = T.optim.Adadelta([y])
z_opt = T.optim.Adadelta([z])

for i in range(n_iter):
  x_opt.zero_grad()
  y_opt.zero_grad()
  z_opt.zero_grad()

  shared_computation = foobar(x, y, z)

  x_loss = f(x, y, z, shared_computation)
  y_loss = g(x, y, z, shared_computation)
  z_loss = h(x, y, z, shared_computation)

  x_loss.backward_with_respect_to(x)
  y_loss.backward_with_respect_to(y)
  z_loss.backward_with_respect_to(z)

  x_opt.step()
  y_opt.step()
  z_opt.step()

My question is how do we do that backward_with_respect_to part in PyTorch? I only want x's gradient w.r.t. x_loss, etc… And then I want all the optimizers to step together (based on the current values of x, y, and z).