Hi,
The autograd computes the gradient for what you give it. So if you backprop for a loss computed with only one branch, it will backprop only that branch.
Note that if you just want to get the sum of the gradients and do a single update, you can do:
lossy = sum(local_loss_list)
# backpropagation
optimizer.zero_grad()
lossy.backward()
# one step of the optmizer (using the gradients from backpropagation)               
optimizer.step()
total_loss = total_loss + lossy