def fit(
        self,
        x: np.ndarray,
        y: np.ndarray,
        validation_data: tuple[np.ndarray, np.ndarray] | None = None,
        batch_size: int = 128,
        nb_epochs: int = 20,
        **kwargs,
    ):
        """
        Train a model adversarially with FBF protocol.
        See class documentation for more information on the exact procedure.

        :param x: Training set.
        :param y: Labels for the training set.
        :param validation_data: Tuple consisting of validation data, (x_val, y_val)
        :param batch_size: Size of batches.
        :param nb_epochs: Number of epochs to use for trainings.
        :param kwargs: Dictionary of framework-specific arguments. These will be passed as such to the `fit` function of
                                  the target classifier.
        """
        logger.info("Performing adversarial training with Fast is better than Free protocol")

        nb_batches = int(np.ceil(len(x) / batch_size))
        ind = np.arange(len(x))

        def lr_schedule(step_t):
            return np.interp([step_t], [0, nb_epochs * 2 // 5, nb_epochs], [0, 0.21, 0])[0]

        logger.info("Adversarial Training FBF")

        for i_epoch in trange(nb_epochs, desc="Adversarial Training FBF - Epochs"):
            # Shuffle the examples
            np.random.shuffle(ind)
            start_time = time.time()
            train_loss = 0.0
            train_acc = 0.0
            train_n = 0.0

            for batch_id in range(nb_batches):
                l_r = lr_schedule(i_epoch + (batch_id + 1) / nb_batches)

                # Create batch data
                x_batch = x[ind[batch_id * batch_size : min((batch_id + 1) * batch_size, x.shape[0])]].copy()
                y_batch = y[ind[batch_id * batch_size : min((batch_id + 1) * batch_size, x.shape[0])]]

                _train_loss, _train_acc, _train_n = self._batch_process(x_batch, y_batch, l_r)

                train_loss += _train_loss
                train_acc += _train_acc
                train_n += _train_n

            train_time = time.time()

            # compute accuracy
            if validation_data is not None:
                (x_test, y_test) = validation_data
                output = np.argmax(self.predict(x_test), axis=1)
                nb_correct_pred = np.sum(output == np.argmax(y_test, axis=1))
                logger.info(
                    "epoch: %s time(s): %.1f l_r: %.4f loss: %.4f acc(tr): %.4f acc(val): %.4f",
                    i_epoch,
                    train_time - start_time,
                    l_r,
                    train_loss / train_n,
                    train_acc / train_n,
                    nb_correct_pred / x_test.shape[0],
                )
            else:
                logger.info(
                    "epoch: %s time(s): %.1f l_r %.4f loss: %.4f acc: %.4f",
                    i_epoch,
                    train_time - start_time,
                    l_r,
                    train_loss / train_n,
                    train_acc / train_n,
                )

        Train a model adversarially with FBF protocol.
        See class documentation for more information on the exact procedure.

        :param x: Training set.
        :param y: Labels for the training set.
        :param validation_data: Tuple consisting of validation data, (x_val, y_val)
        :param batch_size: Size of batches.
        :param nb_epochs: Number of epochs to use for trainings.
        :param kwargs: Dictionary of framework-specific arguments. These will be passed as such to the `fit` function of
                                  the target classifier.
        
art/defences/trainer/adversarial_trainer_fbf_pytorch.py