Neural Pseudo-Label Optimism for the Bank Loan Problem
This addresses a critical issue in sequential decision-making for lenders, offering a novel solution to prevent infinite regret in neural network-based models, though it is incremental as it extends optimism methods from linear to deep learning contexts.
The paper tackles the bank loan problem, where a lender's classification algorithm can get stuck with self-fulfilling false negatives due to missing labels for rejected data, and presents Pseudo-Label Optimism (PLOT), a method for deep neural networks that adds optimistic labels to train an optimistic model, achieving competitive performance on benchmarks and providing a logarithmic regret guarantee under specific conditions.
We study a class of classification problems best exemplified by the \emph{bank loan} problem, where a lender decides whether or not to issue a loan. The lender only observes whether a customer will repay a loan if the loan is issued to begin with, and thus modeled decisions affect what data is available to the lender for future decisions. As a result, it is possible for the lender's algorithm to ``get stuck'' with a self-fulfilling model. This model never corrects its false negatives, since it never sees the true label for rejected data, thus accumulating infinite regret. In the case of linear models, this issue can be addressed by adding optimism directly into the model predictions. However, there are few methods that extend to the function approximation case using Deep Neural Networks. We present Pseudo-Label Optimism (PLOT), a conceptually and computationally simple method for this setting applicable to DNNs. \PLOT{} adds an optimistic label to the subset of decision points the current model is deciding on, trains the model on all data so far (including these points along with their optimistic labels), and finally uses the resulting \emph{optimistic} model for decision making. \PLOT{} achieves competitive performance on a set of three challenging benchmark problems, requiring minimal hyperparameter tuning. We also show that \PLOT{} satisfies a logarithmic regret guarantee, under a Lipschitz and logistic mean label model, and under a separability condition on the data.