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 the DP-InstaHide 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 DP-InstaHide protocol")

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

        logger.info("Adversarial Training DP-InstaHide")

        for i_epoch in trange(nb_epochs, desc="DP-InstaHide training 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):
                # create batch data
                x_batch = x[ind[batch_id * batch_size : min((batch_id + 1) * batch_size, x.shape[0])]]
                y_batch = y[ind[batch_id * batch_size : min((batch_id + 1) * batch_size, x.shape[0])]]

                # augment the data
                x_aug = x_batch.copy()
                y_aug = y_batch.copy()
                for augmentation in self.augmentations:
                    x_aug, y_aug = augmentation(x_aug, y_aug)

                # apply additive noise
                x_aug = self._generate_noise(x_aug)

                # fit batch
                self._classifier.fit(x_aug, y_aug, nb_epochs=1, batch_size=x_aug.shape[0], verbose=False, **kwargs)

                # get metrics
                loss = self._classifier.compute_loss(x_aug, y_aug, reduction="mean")
                output = np.argmax(self.predict(x_batch), axis=1)
                acc = np.sum(output == np.argmax(y_batch, axis=1))
                n = len(x_aug)

                # update metrics
                train_loss += np.sum(loss)
                train_acc += acc
                train_n += 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)
                test_loss = self._classifier.compute_loss(x_test, y_test, reduction="mean")
                test_acc = np.mean(output == np.argmax(y_test, axis=1))
                logger.info(
                    "epoch: %s time(s): %.1f, loss(tr): %.4f, acc(tr): %.4f, loss(val): %.4f, acc(val): %.4f",
                    i_epoch,
                    train_time - start_time,
                    train_loss / train_n,
                    train_acc / train_n,
                    test_loss,
                    test_acc,
                )
            else:
                logger.info(
                    "epoch: %s time(s): %.1f, loss: %.4f, acc: %.4f",
                    i_epoch,
                    train_time - start_time,
                    train_loss / train_n,
                    train_acc / train_n,
                )

        Train a model adversarially with the DP-InstaHide 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/dp_instahide_trainer.py