What do you mean by “its true updated” do you mean the correct gradients for your function? Well they most certainly are not (in the sense that your fonction don’t have proper gradients) otherwise you could just use the autograd to compute them, you would not have to compute them by hand 
I am not familiar with the algorithm you shared above but if you have two models you can loop through model1 parameters then model2 parameters. But that depends on what the algorithm is doing, you’ll need to look into that.