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.
Large language models (LLMs) are increasingly extended into deep search agents that solve complex questions through multi-step interaction with external search and browsing tools. However, existing agents often incur substantial computational and interaction costs, generating lengthy trajectories that contain redundant queries, inefficient exploration, and irrelevant observations. Existing efficiency-oriented methods usually encourage agents to use tools less frequently, but treating all tool interactions uniformly may also suppress steps that gather necessary evidence. In this paper, we propose CRISP, a framework for training efficient deep search agents through critical step perception. Unlike prior efficiency methods that uniformly penalize tool use, CRISP distinguishes interactions that gather necessary evidence from redundant ones and shapes the training reward to preserve the former while pruning the latter, improving efficiency without sacrificing the evidence needed for correct answers. Specifically, CRISP first constructs critical-step labels with Backward Evidence Induction: starting from the final answer, a strong model traverses a completed search trajectory backward and judges whether each tool-interaction step provides or preserves evidence for the final answer. We then distill these step-wise judgments into a smaller critical-step recognizer, enabling full-trajectory analysis in a single pass. During policy optimization, an efficiency-aware reward is applied only to successful rollouts. Experiments on BrowseComp and HLE-Verified show that CRISP maintains competitive final-answer accuracy while reducing average interaction turns by 15.1% and 33.2%, respectively, demonstrating substantial improvements in interaction efficiency.