Not All Entropy Is Equal: Reward-Conditioned Entropy Allocation in Reinforcement Learning with Verifiable Rewards

Song Yu, Li Li, Zhenming Wu

Policy entropy is widely used to diagnose exploration and collapse in reinforcement learning with verifiable rewards (RLVR), yet its magnitude does not consistently track reasoning performance across optimization objectives. We argue that this ambiguity arises because global token entropy conflates uncertainty in successful and failed trajectories, diversity across correct solution strategies, and variation among realizations of the same strategy. We introduce \textbf{Reward-Conditioned Entropy Allocation (RCEA)}, a hierarchical diagnostic framework that separates complete-trajectory entropy from average token entropy, conditions uncertainty on verifier outcome and process validity, measures correct-solution-mode retention, and connects these population-level quantities to local covariance-driven updates. In controlled sweeps over six RLVR objectives at two model scales, entropy trajectories do not induce a stable ordering of reasoning accuracy. Token entropy is higher for verifier-failed than successful trajectories under both broad separately aggregated estimates and a common-question paired analysis, whose confidence intervals exclude equality at 10 of 12 displayed endpoints.…