Abstract
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 \textit{tasks}, \textit{environments}, and \textit{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, \textit{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.
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URL
https://arxiv.org/abs/2610.23946
