How to create my own custom objective function

Question

I've got a bit of a problem on implementing my own custom objective function I'm gonna use for LightGBMClassifier.

I'm trying to reproduce the log loss function (I've read somewhere that is also called cross-entropy or something. Please do correct me about this, I really still don't know a lot.) and use it as my objective function. From what I've read all over the net it seems that it is the default loss function for binary classification and there's really no need to make my own.

This is my codes:

def my_naive_log_loss_function(y_true, y_pred, eps=1e-15):
    y_pred = np.clip(y_pred, eps, 1 - eps)
    return -y_true * np.log(y_pred) - (1 - y_true) * np.log(1 - y_pred)

def my_naive_log_loss_metric(y_true, y_pred):
    loss = np.mean(my_naive_log_loss_function(y_true, y_pred))
    return "my_naive_log_loss_metric", loss, False

def my_naive_log_loss_objective(y_true, y_pred):
    func = lambda z: my_naive_log_loss_function(y_true, z)
    gradient = derivative(func, y_pred, n=1, dx=1e-6)
    hessian = derivative(func, y_pred, n=2, dx=1e-6)
    return gradient, hessian

custom_loss_ens = LGBMClassifier(objective=my_naive_log_loss_objective, boosting_type="dart", n_estimators=100, max_depth=10, random_state=42)
custom_loss_ens.fit(X_train, y_train)

When I call custom_loss_ens.predict(X_val) it throws an error Cannot compute class probabilities or labels due to the usage of customized objective function. Returning raw scores instead. _log_warning("Cannot compute class probabilities or labels ")

and just outputs an array of zeros.

How can I do this properly?