Signed compression progress on sealed audit defeats Goodhart's law

A new paper from Ayush Mittal and Dhruv Gupta provides a formal proof that using signed compression progress on a sealed audit as an intrinsic reward for AI agents is resistant to Goodhart's law. The key idea: reward the agent by the signed decrease in loss on a fixed, sealed set of audit data. This makes cumulative reward telescope exactly to the improvement on that audit from start to end, so no policy can push reward up indefinitely while true performance stagnates. For finite audit sets, the bound becomes true improvement plus 2Δ_n, where Δ_n is the uniform audit deviation of the model class — a horizon-free guarantee independent of time. The paper also rigorously catalogs failure modes: clipping, stream leakage, and reusable audits can break the guarantee, but signed progress on a sealed audit remains robust.

The authors back their theory with a Lean 4 mechanization of the structural core and experiments on ARC-TGI grid-transformation generators with adaptive holdout attacks. They show that finite-audit deviation scales as n^{-0.527}, signed progress resists clip-farming and noisy-TV curiosity, and naive reusable audits are exploitable by black-box scalar feedback while standard release defenses keep attacks below the 2Δ_n threshold. This work provides a practical, theoretically grounded way to design intrinsic rewards that reliably signal genuine learning, with direct implications for safe AI training and agent alignment.