Evaluator Ensembles Under Reward Hacking: Covariance Geometry and Finite-Search Guarantees
Language-model judges and reward models enable scalable supervision, but finite optimization can exploit evaluator errors rather than improve response quality. We characterize this failure through the covariance geometry of evaluator ensembles. For calibrated judges, the ensemble mean retains common-mode error along the all-ones direction, whereas cross-judge disagreement captures only orthogonal error. Consequently, disagreement can be high despite robust aggregation, or low while shared response-dependent errors persist. We prove that common-mode error is not identifiable from internal judge scores alone. Under a joint sub-Gaussian model, we bound best-of-K selection overstatement and t...
| Authors | Fariya Afrin, Ibne Farabi Shihab |
|---|---|
| Primary category | cs.LG |
| Published | 8 August 2026 |
| Last updated at source | 8 August 2026 |
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