CUDA Out of memory when using autogrid to do multiple round of back propagation

I’m trying to train a function f of weights w that takes in some inputs x and outputs y. The loss function is MSELoss()(y, target). Now I want to optimize f such that given a random x input, we can optimize x so as to minimize the loss function. This means that for a random initial guess, f should be optimized so as to most quickly find the solution x through gradient updates. The code looks like this:

    initial_x = torch.Tensor()
    opt = optim.Adam([initial_x], lr=0.001)
    opt2 = optim.Adam([w], lr=0.001)
    for i in range(10):
         y = f(w, initial_x)
         loss = MSELoss()(y, target)
         initial_x.grad = torch.autograd.grad(loss, initial_x, retain_graph=True, create_graph=True)[0]
    loss = MSELoss(f(w, initial_x), target)

however, this would make the occupied memory to grow. any fix?