IsoCompute Playbook: Optimally Scaling Sampling Compute for LLM RL

Abstract

While scaling laws guide compute allocation for LLM pre-training, analogous prescriptions for reinforcement learning (RL) post-training of large language models (LLMs) remain poorly understood. We study the compute-optimal allocation of sampling compute for on-policy RL methods in LLMs, framing scaling as a compute-constrained optimization over three resources: parallel rollouts per problem, number of problems per batch, and number of update steps. We find that the compute-optimal number of parallel rollouts per problem increases predictably with compute budget and then saturates. This trend holds across both easy and hard problems, though driven by different mechanisms: solution sharpening on easy problems and coverage expansion on hard problems. We further show that increasing the number of parallel rollouts mitigates interference across problems, while the number of problems per batch primarily affects training stability and can be chosen within a broad range. Validated across base models and data distributions, our results recast RL scaling laws as prescriptive allocation rules and provide practical guidance for compute-efficient LLM RL post-training.

Figures (27)

• Figure 1: Compute-optimal sampling for LLM RL. We study allocation of sampling compute along three axes: parallel rollouts per problem ($n$), problems per batch ($B_{\text{p}}$), and sequential iterations ($M$), where the total compute is $C = B_{\text{p}} \cdot n \cdot M$. We find that: (1) optimal number of rollouts $n$ increases with the compute budget $C$; (2) easy and hard problem sets exhibit similar scaling trends but arise from different underlying mechanisms; (3) under a constraint on $B = B_{\text{p}} \cdot n$, the optimal strategy prioritizes larger $B_{\text{p}}$ (smaller $n$) at low compute budgets, and shifts toward larger $n$ (smaller $B_{\text{p}}$) at high compute budgets to maximize performance; and (4) $B_{\text{p}}$ has only a marginal effect on performance when kept within a moderate range.
• Figure 2: Difficulty distribution of Easy vs. Hard problems. We split problems into Easy and Hard sets according to pass@16 (average pass rate over 16 generations per problem).
• Figure 3: Regularization ablations on Easy and Hard. On the Easy set, standard KL+Entropy regularization achieves the best reward. On the Hard set, these regularizers destabilize training even with zero-variance filtering; disabling them yields significantly more stable optimization and higher reward.
• Figure 4: LR scaling strategy. Square-root scaling ($\sqrt{B}$) outperforms linear and constant scaling at large batch sizes ($B=8192$).
• Figure 5: Illustration of record-breaking points. Gray dots show validation reward points from multiple training runs, while orange dots mark record-breaking points, defined as the earliest (smallest compute) points that enter a higher discretized reward bin than all previous points. The dashed curve shows the monotonic fit over the retained points on the performance frontier.