Deep search agents operate over trajectories spanning dozens of steps, yet standard reinforcement learning provides only a single outcome reward per trajectory, which is far too sparse for effective credit assignment. On-policy self-distillation (OPSD) addresses this by using the model's own logits as dense token-level teachers, but extending it to search agents introduces a fundamental tension: the teacher, having access to privileged information such as the correct answer, produces a distribution that differs systematically from the student's exploration-based reasoning, and naive distillation causes the student to inherit this information asymmetry rather than learn better search strategies. We resolve this tension through two contributions. First, we construct Evidence Anchors, which are concise, step-level evidence snippets extracted from the web, as privileged information that captures key reasoning steps without revealing the entire answer path. Second, we propose Step-Level Self-Distilled Policy Optimization (SSPO), which converts teacher-student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories. This design decouples what to update from how much to update: the outcome reward determines the direction of policy change, while the teacher modulates its magnitude at each step. Correct trajectories are left untouched, preserving their diversity. On Qwen3-8B, SSPO consistently outperforms GRPO across BrowseComp, GAIA, and FRAMES, surpassing or matching GRPO trained with twice as many gradient steps while adding only about 5 percent overhead per step from a single additional forward pass.
With the rapid advancement of large language models (LLMs), modern systems not only possess strong foundational capabilities and extensive knowledge, but can also solve complex problems via long, multi-step reasoning. However, as reasoning traces become longer, LLMs may produce a substantial amount of hallucinated content during the reasoning process, which is often difficult to detect. In this work, we conduct a fine-grained analysis of hallucinations arising in LLM reasoning and find that the reasoning traces are particularly prone to Context-Sensitive Factual Hallucinations: cases where the model actually has the relevant knowledge, yet makes factual errors due to contextual interference during reasoning. To address this issue, we propose Step-level Self-Consistency Group Relative Policy Optimization (SSC-GRPO), which assigns step-level rewards to reasoning traces by computing self-consistency scores of individual steps across multiple rollouts. Compared with prior methods, SSC-GRPO achieves state-of-the-art performance on both mathematical reasoning benchmarks and hallucination leaderboards. Our results offer a new perspective for detecting and mitigating hallucinations in the reasoning process of large language models.