from iftopt import HyperOptimizer
train_lr = val_lr = 0.1
# parameter to minimize the training loss
x = torch.nn.Parameter(...)
# hyper-parameter to minimize the validation loss
y = torch.nn.Parameter(...)
# training loss optimizer
opt = torch.optim.SGD([x], lr=train_lr)
# validation loss optimizer
hopt = HyperOptimizer(
    [y], torch.optim.SGD([y], lr=val_lr), vih_lr=0.1, vih_iterations=5)
# outer optimization loop for y
for _ in range(...):
    # inner optimization loop for x
    for _ in range(...):
        z = train_loss(x, y)
        # inner optimization step for x
        opt.zero_grad()
        z.backward()
        opt.step()
    # outer optimization step for y
    hopt.set_train_parameters([x])
    z = train_loss(x, y)
    hopt.train_step(z)
    v = val_loss(x, y)
    hopt.val_step(v)
    hopt.grad()
    hopt.step()

train_loss = lambda x, y: (x + y) ** 2
val_loss = lambda x, y: x ** 2