The cost function used is the negative log likelihood (NLL) of the GP predictions, which quantifies the discrepancy between the model's predictions and the observed targets. Although we do not explicitly implement a separate acquisition function for active data selection, the NLL-and implicitly, the residual variance computed during training-serves as an uncertainty measure that can guide data selection. In our implementation, training data are sampled in mini-batches, and early stopping based on validation NLL is employed to avoid overfitting.