# IsoCompute Playbook: Optimally Scaling Sampling Compute for LLM RL

arXiv: https://arxiv.org/abs/2603.12151 · HTML: https://mlsanity.com/paper/2603.12151/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 28 of 28)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer](https://mlsanity.com/paper/2203.03466/) (2022)
- [An Empirical Model of Large-Batch Training](https://mlsanity.com/paper/1812.06162/) (2018)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [The Art of Scaling Reinforcement Learning Compute for LLMs](https://mlsanity.com/paper/2510.13786/) (2025)
- [RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold](https://mlsanity.com/paper/2406.14532/) (2024)
- [Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective](https://mlsanity.com/paper/2506.14965/) (2025)
- [How Does Critical Batch Size Scale in Pre-training?](https://mlsanity.com/paper/2410.21676/) (2024)
- [Scaling Scaling Laws with Board Games](https://mlsanity.com/paper/2104.03113/) (2021)
- [RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environments](https://mlsanity.com/paper/2511.07317/) (2025)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [POPE: Learning to Reason on Hard Problems via Privileged On-Policy Exploration](https://mlsanity.com/paper/2601.18779/) (2026)
- [Scaling laws for single-agent reinforcement learning](https://mlsanity.com/paper/2301.13442/) (2023)
- [Ray Interference: a Source of Plateaus in Deep Reinforcement Learning](https://mlsanity.com/paper/1904.11455/) (2019)
- [Scaling Behaviors of LLM Reinforcement Learning Post-Training: An Empirical Study in Mathematical Reasoning](https://mlsanity.com/paper/2509.25300/) (2025)
- [BroRL: Scaling Reinforcement Learning via Broadened Exploration](https://mlsanity.com/paper/2510.01180/) (2025)
- [Knapsack RL: Unlocking Exploration of LLMs via Optimizing Budget Allocation](https://mlsanity.com/paper/2509.25849/) (2025)
- [Value-Based Deep RL Scales Predictably](https://mlsanity.com/paper/2502.04327/) (2025)
- [Stochastic Gradient Succeeds for Bandits](https://mlsanity.com/paper/2402.17235/) (2024)

## Built on by (most cited first, 6 of 6)

- [Understanding Reasoning from Pretraining to Post-Training](https://mlsanity.com/paper/2607.16097/) (2026)
- [Nudging Beyond the Comfort Zone: Efficient Strategy-Guided Exploration for RLVR](https://mlsanity.com/paper/2605.15726/) (2026)
- [TailSFT: Filtered Fine-Tuning Improves Post-Training Performance](https://mlsanity.com/paper/2608.25756/) (2026)
- [When Do Larger Batches Help Scale LLM Reinforcement Learning?](https://mlsanity.com/paper/2608.29296/) (2026)
- [Manifold Bandits: Bayesian Curriculum Learning over the Latent Geometry of Large Language Models](https://mlsanity.com/paper/2606.19750/) (2026)
- [Scaling of Capability and Efficiency at Inference Time in Large Reasoning Models](https://mlsanity.com/paper/2609.27166/) (2026)

## Abstract (arXiv)

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.