Detailed analysis of RLVR’s mechanism for selecting optimal reasoning patterns in non-convex LLM policies

Develop a detailed analysis of how Reinforcement Learning with Verifiable Rewards (RLVR) enables large language models with non-convex autoregressive policies to find and select optimal reasoning patterns for a given question, providing training-dynamics and convergence guarantees in the general LLM setting beyond the simplified tabular policy parameterization.

Background

The paper models reasoning in LLMs as a two-step process of selecting a reasoning pattern and then generating an answer, and shows theoretically (Theorem 5.2) that the KL-constrained RLVR objective favors higher-success-rate patterns. However, because general autoregressive LLM policies are non-convex, the authors restrict their detailed training-dynamics analysis to a simplified tabular policy setting.

They explicitly note that providing a more detailed analysis for the general non-convex policy case remains unclear, identifying a gap between the optimal-policy characterization and practical optimization guarantees for real LLMs. Addressing this would clarify how RLVR facilitates selection of optimal reasoning patterns in full-fledged transformer policies and establish broader convergence guarantees.