So I'm basically trying to fit a regression on the relation of the input and output of a neural network model. Then the idea is, that these estimated regression weights should be optimized to some specific target value (let's say matrix of ones). So the weights are optimized, but have a direct relation to the neural network weights. For a simple problem, I can find a solution on paper, but I fail to implement this. The loss is not decreasing, but oscillating.
# Some arbitrary PyTorch model my_nn = Net() # Our target regression weights target = torch.ones(2, 2) # Optimizer for NN weights optimizer = optim.Adam(my_nn.parameters(), lr=0.0001) # Arbitrary loss function criterion = nn.MSELoss() # Training loop my_nn.train() for epoch in range(500): print('Running Epoch: ', epoch) # zero the parameter gradients optimizer.zero_grad() # output of model is 2-dim y_pred = my_nn(X) # weights for regression model w1 = Variable(torch.randn(2, 2).type(torch.float), requires_grad=True) # optimizer for regression model optimizer1 = optim.SGD([w1], lr=0.001, momentum=0.9) for nest_epoch in range(1000): optimizer1.zero_grad() y_hat = torch.mm(X, w1) loss = criterion(y_hat, y_pred) # Need to add retain_graph, as it doesn't work otherwise # but it does work, this loss will get close to 0 loss.backward(retain_graph=True) optimizer1.step() # this loss does not decrease loss = criterion(target, w1) print('Loss:', loss.item()) loss.backward() optimizer.step() ```