Search-augmented LM agents are typically trained with a binary exact-match reward, which throws away most of what a failed trajectory tells us about why it failed. We introduce HindSearch, a hindsight self-distillation procedure for GRPO: after each rollout, a frozen judge writes a short critique of every failed trajectory using the gold answer, and the critique supplies an auxiliary on-policy distillation signal on the student's search actions. On the standard seven-benchmark suite with Qwen2.5-3B-Instruct, HindSearch reaches 39.4% average EM, outperforming prior search-RL baselines. Removing the judge's access to the gold answer erases most of the gain, isolating hindsight as the source of the improvement.

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