Why can't a loan-approval model learn anything from the applicants it rejected?

## The structure of the problem A credit decision is a one-shot action with bandit feedback, and an unusually harsh version of it. There are two actions, approve and deny. Approve and you eventually observe a reward: repaid, or defaulted. Deny and you observe nothing — the applicant does not half-repay, does not partially default, simply leaves no outcome behind. The feedback is one-sided, which is why the term **selective labels** is used for it: the labels you hold were selected into existence by the very policy you are trying to improve on. ## What the historical table actually contains Suppose a lender has ten years of applications. The outcome column is populated only for the approved rows. If the incumbent policy approved everyone above a credit-score cutoff, the labelled data is essentially the population above that cutoff. A model fitted there can be genuinely excellent at ranking risk among applicants who look like past approvals. It has no evidence whatsoever about what happens below the cutoff, because nobody below it was ever funded. The practical trap is that this weakness is invisible in normal evaluation. Hold out a slice of history, fit, measure — the numbers look fine, because the holdout is drawn from the same approved region. A high AUC on historical approvals means the model ranks approved applicants well. It says nothing at all about applicants the old policy rejected, and a proposal to lower the cutoff is a proposal to operate exactly there. ## The unobserved-signal problem Selective labels get sharper when a human is in the loop. Say officers could approve or deny against the score, using things never entered into the system: a conversation, a document, local knowledge. Then among applicants who share identical recorded features, the ones who were approved are systematically the better ones on the unrecorded signal. The observed default rate for that feature profile is therefore better than the profile deserves on its own. A model fitted to those outcomes learns an optimistic relationship, and when it is deployed to decide *without* the officer, the applicants it approves are an average draw from the profile rather than the hand-picked subset — so realised defaults come in worse than the backtest promised. The same mechanism makes naive human-versus-model comparisons misleading. The model appears to beat the officers on the approved set because it is being graded only on cases the officers chose to fund. ## The wrong fixes Two shortcuts are common and both are defects. The first is labelling every rejected applicant as a default. That invents a label: some rejections would have repaid, and the model is trained to reproduce the old policy's boundary rather than the underlying risk. The second is imputing outcomes for rejections from their nearest approved neighbours. Near the boundary that borrows from a genuinely different population; far from it there are no neighbours at all, and the imputation is just the model's own extrapolation fed back to itself as if it were data. Retraining on the same approved population, however often, changes nothing — the missing region stays missing, and each cycle narrows the funded population a little further. ## What actually works The honest answer is that the missing evidence has to be bought, not derived. - **Randomised approvals.** Fund a small, deliberately chosen share of applicants the current policy would deny, ideally concentrated in the band just below the cutoff where a policy change is plausible. Those loans are expected to lose money; that loss is the price of the only unconfounded data about the region, and it should be budgeted as a data-acquisition cost with a cap. - **Log the decision, not just the outcome.** Record what was decided, by which policy version, on which score, and whether a human overrode it. Without that, you cannot even tell later which rows were policy-selected. - **External outcomes where they exist.** In some markets, an applicant you denied is funded elsewhere, and their subsequent repayment behaviour is observable through shared reporting. That is partial and biased in its own way, but it is real evidence about the rejected region. - **Be explicit about identification.** Present risk in the rejected region as unidentified rather than predicted, and roll a policy change out as a staged expansion of the cutoff, measuring realised performance at each step, rather than a single jump justified by backtest numbers computed where no relevant data exists. ## Why this generalises The pattern recurs wherever a gate decides who generates an outcome: which candidates get interviewed and then rated, which patients get treated and then followed up, which transactions get let through and then observed for fraud. In each case the model's own past decisions determine which rows of the future training set are ever filled in, and the only durable escape is to deliberately let some traffic through the gate at random and pay for what that teaches you.