Better Policies, Worse Verifier Audits

Daniel Cieślak, Jacek Łubiński

Verifier stacks increasingly sit inside post-training and test-time compute loops. We study a specific control loop: a component verifier is evaluated on fresh policy outputs against the full success label and refreshed when that aggregate score falls. For a conjunctive target $y = F \wedge M$, its on-policy AUC is $(1-q)A_{\mathrm{own}} + qA_{\mathrm{cross}}$, where $q = \Pr[F=1 \mid y=0]$. As the policy masters $F$, $q$ can rise toward one, removing weight from $F$-failures and rewarding information about $M$. We call this on-policy audit collapse. We derive a sharp identified set, a complete-erasure threshold, and the exact point at which the audit can prefer a worse component verifier; its population optimum is the full-outcome predictor, not the component oracle. An exact oracle exhibits the collapse, a natural multi-label text control shows inversion can select a head with lower canonical $F$-AUC at the observed failure mixture, and a prediction-registered ECG study shows that acting on the audit can reduce off-policy $F$-AUC, transfer the damage to an unseen generator, and increase downstream constraint violations. Preserving own-failure support prevents the damage.…