There Is No Free Lunch in RLVR: Every pass@1 Gain Has a pass@k Price
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The paper proves that in reinforcement learning with verifiable rewards (RLVR), any improvement in pass@1 necessarily incurs a cost in pass@k, establishing a precise price for such gains. By modeling RLVR as an exponential tilt of a base policy, the authors show that every update that raises pass@1 strictly lowers success on at least one prompt, and that the number of pass@k crossovers is bounded by the sign variation of per‑prompt success shifts. The work also derives an entropy‑performance law and provides a diagnostic to measure this price from evaluation logs.
arXiv:2606. 15455v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) has become a key approach for enhancing the reasoning abilities of large language models.
arXiv:2607. 20543v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) can improve one-sample accuracy while making a model worse under repeated sampling.
The paper introduces Exploration-Distillation (ExpDis), a method that separates exploration from optimization in reinforcement learning with verifiable rewards (RLVR) for language models. ExpDis trains explorer policies with a novelty bonus, filters their outputs for correctness, and distills the results into a student policy that is optimized without the novelty bonus. This iterative process enables aggressive exploration while preserving model quality, outperforming DAPO on multiple mathematical reasoning benchmarks and improving pass@$k$ scaling.
arXiv:2609.01274v1 Announce Type: new Abstract: Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but how these gains relate to inference-time decoding and sear...
The paper investigates how entropy behaves in reinforcement learning with verifiable rewards (RLVR) when the sampling method used during rollouts differs from the learner’s policy. It shows that a constant advantage shift alters the entropy of a softmax policy in a way that depends on the sampler: positive shifts sharpen the policy for samplers whose likelihood ratio increases with token probability (e.g., top‑k, top‑p, min‑p, and temperatures below one) and flatten it for flatter samplers. In group‑based RLVR with token‑level losses, the entropy drift is governed by the token‑weighted net advantage and a covariance term that can amplify over long horizons, with empirical results on 2B and 9B models demonstrating how different sampling and baseline strategies affect entropy stability and held‑out accuracy.