An Empirical Study of Reinforcement Learning Scaling Laws

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.

Pretraining scaling laws treat training data as a one-dimensional quantity: a token count. Agentic reinforcement learning (RL) inherits this scalar abstraction, but modern synthesis pipelines now generate tasks, environments, and trajectories independently and at very different costs, turning data into a structured design space. This raises a question pretraining never had to answer: given a synthesis budget, which axis should be scaled? We address this question end-to-end with three tightly coupled contributions. First, we decompose agentic data into three cardinality axes (task, environment, trajectory), plus a reward-density control variable, and fit per-axis scaling relations on different large language models (LLMs) across math+code, SWE, web, and UI/tool application domains. Across all model sizes, model families, domains, and RL algorithms (PPO and GRPO) we measured, the scaling exponents order as environment $>$ task $>$ trajectory. When environment diversity is decomposed into world and environment-structure diversity, its advantage is mainly driven by the former, while the latter is just comparable to the task diversity. Second, we use the fitted laws as a common ruler to price synthesis methods, capturing each method's efficiency as a per-axis discount factor and identifying critical synthetic-to-real ratios at which collapse begins; these ratios differ by an order of magnitude across axes. Third, we cast budget allocation as a constrained optimization under our laws and discounts, deriving a Chinchilla-style compute-optimal recipe and validating it at held-out scale. The empirical results demonstrate that following the recipe yields up to $1.7\times$ compute efficiency over the dominant ``scale-the-trajectories'' practice.

Scaling laws predict large-model performance from small experiments, but finding a reliable law itself requires costly experiments. SLDBench tests whether language-model agents can discover scaling laws when all experimental results are given upfront. We introduce SLDBench v2 with two extensions. First, we expand the corpus from 8 to 127 scenarios spanning language-model pretraining, downstream performance, and vision-language transfer, and select 30 challenging scenarios on which a reference power-law fit reaches $R^2 \le 0.8$; they represent at least $1.09 \times 10^{23}$ FLOPs of source-reported training compute. Second, we introduce active scaling law discovery: an agent chooses which experiments to run, pays each one's recorded cost (e.g., training FLOPs), and revises its law as outcomes arrive, and is scored on the same hidden extrapolation targets as in the passive setting. Across 8 frontier agent systems, median $R^2$ drops from 0.72-0.75 (passive) to 0.24-0.57 (active), and prediction error rises 1.5-4.7 times, depending on the system. Agents favor cheap experiments, spending 8-44% of the full-pool cost on average; low-cost acquisition can yield strong predictions, but cheap purchases also leave experimental conditions needed for extrapolation unobserved. Experimental planning thus remains a key open challenge for agents that assist model development in the prevailing AI-for-AI study. Project page: https://lingbei-meng.github.io/SLDBench-v2/.