SD-Search: Hindsight Self-Distillation for Search-Augmented Reasoning

Search-augmented reasoning agents interleave internal reasoning with calls to an external retriever, and their performance relies on the quality of each issued query. However, under outcome-reward reinforcement learning, every search decision in a rollout shares the same trajectory-level reward, leaving individual queries without step-specific credit. Recent process-supervision approaches address this gap by drawing step-level signals from outside the policy, relying either on a much larger teacher model, or on sub-question annotations produced by a stronger external system. In contrast, we propose \textbf{SD-Search}, which derives step-level supervision \emph{from the policy itself} through hindsight self-distillation, requiring neither an external teacher nor additional annotations. In SD-Search, a single model plays two roles that differ only in conditioning: a student that sees only the context available at inference time, and a teacher that additionally conditions on a compact hindsight block summarizing the search queries and final outcomes of a group of rollouts sampled from the same question. Since teacher knows how each rollout unfolded and which ones succeeded, its query distribution implicitly marks which decisions were worth making, and the student is trained to recover this behavior by minimizing the token-level Jensen--Shannon divergence to the teacher at search-query positions. This layers a dense, step-level signal on top of GRPO's coarse trajectory reward. Crucially, this signal requires only a single teacher forward pass per rollout at training time, all absorbed within the standard RL loop without external model inference, auxiliary annotation pipeline, or additional training. On seven single-hop and multi-hop QA benchmarks, SD-Search reaches $0.428$ average Exact Match with Qwen2.5-3B, matching the leading process-supervision baseline without its external teacher, and $0.476$ with Qwen2.5-7B, surpassing all outcome-reward and process-supervision baselines on the average.