Reinforcement Learning (RL) has emerged as a dominant paradigm for eliciting long-horizon reasoning in Large Language Models (LLMs). However, scaling Tool-Integrated Reasoning (TIR) via RL remains challenging due to interaction collapse: a pathological state where models fail to sustain multi-turn tool usage, instead degenerating into heavy internal reasoning with only trivial, post-hoc code verification. We systematically study three questions: (i) how cold-start Supervised Fine-Tuning (SFT) induces an agentic, tool-using behavioral prior, (ii) how teacher-trajectory structure and interaction density shape exploration and downstream RL outcomes, and (iii) how the RL interaction budget affects learning dynamics and generalization under varying inference-time budgets. We then introduce ASTER (Agentic Scaling with Tool-integrated Extended Reasoning), a framework that circumvents this collapse through a targeted cold-start strategy prioritizing structured, interaction-dense trajectories. We find that a small expert cold-start set of just 4K structurally rich, interaction-dense trajectories yields the strongest downstream performance, establishing a robust prior that enables superior exploration during extended RL training. Extensive evaluations demonstrate that ASTER-4B achieves strong results on competitive mathematical benchmarks, reaching 89.6% mean accuracy on AIME2025 and remaining competitive with leading frontier open-source models. See more details at https://github.com/CodeByLeo-bit/ASTER.

In Reinforcement Learning from Human Feedback (RLHF), the reward model (RM) evaluates the response quality based on the given context and assigns a reward. It plays a crucial role in aligning RLHF with human preferences. Although the current RM training paradigm concatenates the context and response while amplifying the reward difference between good and bad response pairs, we demonstrate that the RM faces two significant issues: i) it often allocates only a small proportion of attention to the context, and ii) it frequently ignores segments of the context that are relevant for evaluating the response quality. These issues undermine the RM’s effectiveness in modeling human preferences. To further address these challenges, we propose AttnRM, a novel optimization framework that enables the RM to concentrate on crucial segments of the context. Experimental results demonstrate that AttnRM significantly improves preference modeling by increasing attention to relevant information within the context. It also enhances the RM’s generalizability and achieves better performance in aligning with human preferences.