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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.07114 |
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| _version_ | 1866918489167495168 |
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| author | Wang, Tao Li, Shuo Sun, Yan Ding, Dongsheng Dobriban, Edgar |
| author_facet | Wang, Tao Li, Shuo Sun, Yan Ding, Dongsheng Dobriban, Edgar |
| contents | Reinforcement learning with verifiable rewards (RLVR) has emerged as a central paradigm for improving the reasoning capabilities of large language models. Group-based policy optimization methods, such as GRPO, typically allocate a fixed number of rollouts to every prompt. This uniform allocation can be inefficient: it over-allocates compute to prompts whose sampled groups are already saturated while under-exploring prompts for which additional samples may reveal useful correct trajectories. To address this limitation, we introduce hit utility, the posterior probability that at least one rollout in a proposed additional allocation for a prompt will be correct. Building on this notion, we propose Hit-Utility Optimal Rollout Allocation (HORA), a learning-free rollout allocation policy that maximizes total posterior hit utility within each allocation batch. HORA adaptively reallocates rollout budgets while leaving the downstream reward evaluation and group-based advantage estimator unchanged. Across four mathematical reasoning benchmarks and three model scales, HORA preserves comparable Pass@1 and improves Pass@K over compute-matched GRPO in ten of twelve model--benchmark configurations, with one tie and one saturated exception. It is also drop-in compatible with other group-based estimators such as RLOO. Ablation studies indicate that the uniform prior used by HORA is competitive with five prompt-conditioned learned-prior alternatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07114 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Where to Spend Rollouts: Hit-Utility Optimal Rollout Allocation for Group-Based RLVR Wang, Tao Li, Shuo Sun, Yan Ding, Dongsheng Dobriban, Edgar Machine Learning Reinforcement learning with verifiable rewards (RLVR) has emerged as a central paradigm for improving the reasoning capabilities of large language models. Group-based policy optimization methods, such as GRPO, typically allocate a fixed number of rollouts to every prompt. This uniform allocation can be inefficient: it over-allocates compute to prompts whose sampled groups are already saturated while under-exploring prompts for which additional samples may reveal useful correct trajectories. To address this limitation, we introduce hit utility, the posterior probability that at least one rollout in a proposed additional allocation for a prompt will be correct. Building on this notion, we propose Hit-Utility Optimal Rollout Allocation (HORA), a learning-free rollout allocation policy that maximizes total posterior hit utility within each allocation batch. HORA adaptively reallocates rollout budgets while leaving the downstream reward evaluation and group-based advantage estimator unchanged. Across four mathematical reasoning benchmarks and three model scales, HORA preserves comparable Pass@1 and improves Pass@K over compute-matched GRPO in ten of twelve model--benchmark configurations, with one tie and one saturated exception. It is also drop-in compatible with other group-based estimators such as RLOO. Ablation studies indicate that the uniform prior used by HORA is competitive with five prompt-conditioned learned-prior alternatives. |
| title | Where to Spend Rollouts: Hit-Utility Optimal Rollout Allocation for Group-Based RLVR |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.07114 |