Towards Better RL Training Data Utilization via Second-Order Rollout

Reinforcement learning (RL) has become a central post-training tool for improving the reasoning abilities of large language models (LLMs). In these systems, the rollout, the trajectory sampled from a prompt to termination, including intermediate reasoning steps and optional tool or environment interactions, determines the data the optimizer learns from, yet rollout design is often underreported. This survey provides an optimizer-agnostic view of rollout strategies for RL-based post-training of reasoning LLMs. We formalize rollout pipelines with unified notation and introduce Generate-Filter-Control-Replay (GFCR), a lifecycle taxonomy that decomposes rollout pipelines into four modular stages: Generate proposes candidate trajectories and topologies; Filter constructs intermediate signals via verifiers, judges, critics; Control allocates compute and makes continuation/branching/stopping decisions under budgets; and Replay retains and reuses artifacts across rollouts without weight updates, including self-evolving curricula that autonomously generate new training tasks. We complement GFCR with a criterion taxonomy of reliability, coverage, and cost sensitivity that characterizes rollout trade-offs. Using this framework, we synthesize methods spanning RL with verifiable rewards, process supervision, judge-based gating, guided and tree/segment rollouts, adaptive compute allocation, early-exit and partial rollouts, throughput optimization, and replay/recomposition for self-improvement. We ground the framework with case studies in math, code/SQL, multimodal reasoning, tool-using agents, and agentic skill benchmarks that evaluate skill induction, reuse, and cross-task transfer. Finally, we provide a diagnostic index that maps common rollout pathologies to GFCR modules and mitigation levers, alongside open challenges for building reproducible, compute-efficient, and trustworthy rollout pipelines.

The effectiveness of Reinforcement Learning (RL) in Large Language Models (LLMs) depends on the nature and diversity of the data used before and during RL. In particular, reasoning problems can often be approached in multiple ways that rely on different forms of reasoning, and exposure to only a limited range of such approaches in the training data may limit the effectiveness of RL. Motivated by this, we investigate using diverse self-generated data during mid-training as an intermediate step before RL training. Specifically, we adopt a bootstrapped data-generation framework guided by George Polya's problem-solving approaches for generating multiple variants of correct answers for each question in the training data, and then perform fine-tuning. We first provide a theoretical perspective on how mid-training on such data improves RL and explain how policy-gradient updates can incentivize combining multiple approaches. We then empirically demonstrate that RL-trained models initialized with our mid-training data achieve consistent improvements across various mathematical reasoning benchmarks and other OOD tasks like code generation and narrative reasoning. Overall, our investigative study shows that a language model learning multiple problem-solving approaches, through self-generated data helps subsequent RL.

Reinforcement learning (RL) has emerged as a powerful paradigm for improving large language models beyond supervised fine-tuning, yet sustaining performance gains at scale remains an open challenge, as data diversity and structure, rather than volume alone, become the limiting factor. We address this by introducing a scalable multi-turn synthetic data generation pipeline in which a teacher model iteratively refines problems based on in-context student performance summaries, producing structured difficulty progressions without any teacher fine-tuning. Compared to single-turn generation, this multi-turn approach substantially improves the yield of valid synthetic problems and naturally produces stepping stones, i.e. easier and harder variants of the same core task, that support curriculum-based training. We systematically study how task difficulty, curriculum scheduling, and environment diversity interact during RL training across the Llama3.1-8B Instruct and Qwen3-8B Base model families, with additional scaling experiments on Qwen2.5-32B. Our results show that synthetic augmentation consistently improves in-domain code and in most cases out-of-domain math performance, and we provide empirical insights into how curriculum design and data diversity jointly shape RL training dynamics.