Did you get the transfer learning tutorial working ? what were you doing wrong ?
For your question, You can do it either way creating 2 optimizers and updating individually or creating groups and setting values in the groups like
optimizer = torch.optim.SGD([{'params': filter(lambda p: p.requires_grad, model.features.parameters()), 'lr':1e-4, },
                             {'params': filter(lambda p: p.requires_grad, model.classifier.parameters())}], lr=1e-3, momentum=0.95, weight_decay=1e-5)

you can set parameters specific to every part of your model like above. And the values outside the list are like default values, will be used if not specifically set.