Advantage Scale Calibration Imbalance in Group-Relative Optimization under Low-Variance Rewards: Diagnosis and Bounded Recovery

Abstract:In verifier-style RLVR, group-relative optimization often treats advantage scale as an implementation detail. This paper separates two low-variance cases: sub-resolution jitter that should not become a preference signal, and credible but small cardinal gaps that should be learned without distorting KL calibration. We propose an advantage-scale three-way calibration interface: the same within-group scale denominator simultaneously determines the reward-branch strength, prompt-level batch weight, and the effective KL calibration induced when the reward branch is re-expressed on the original cardinal scale. This interface explains why RLOO / this http URL can let credible small gaps become KL dominated, whereas GRPO's standard-deviation denominator can amplify tiny gaps without bound. Based on this interface, we further introduce the Reward-Resolution Protocol and MaxNorm-AC, respectively filtering sub-resolution gaps and providing bounded cardinal recovery on credible nonzero gaps. Across dense / MoE architectures and math / code reasoning, MaxNorm-AC improves over the strongest robust-scale baseline while truncating the low-variance inverse-scale tail.

Computation and Language (cs.CL); Machine Learning (cs.LG)

arXiv:2609.19164 [cs.CL]

(or arXiv:2609.19164v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2609.19164 Focus to learn more arXiv-issued DOI via DataCite

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