MaPP: A Unified Marginalized Posterior-Predictive Framework for Data-Efficient RLVR

Yangyang Ren, Haodong Zhu, Sheng Xu, Yanjing Li, Nikolai Yu. Zolotykh +2

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models but incurs substantial costs from rollouts and policy updates. Online prompt selection improves efficiency by using per-prompt Bayesian posteriors to predict difficulty and prioritize informative prompts. However, existing methods overlook how reliably learning signals are extracted from sampled responses. In GRPO, a response's advantage depends on both its own outcome and the randomly sampled outcomes of its peers through group normalization. Our theoretical and experimental analyses show that uncertainty in group composition introduces composition noise, a non-vanishing variance component that imposes an irreducible lower bound on gradient estimation error and impairs downstream prompt selection. We propose MaPP (Marginalized Posterior-Predictive), a unified framework for data-efficient RLVR that denoises response-level advantage estimation and improves prompt selection using a shared Beta posterior. For each response, MaPP replaces the standard group-relative advantage with a composition-invariant intrinsic advantage through closed-form Beta-Binomial…