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.
Outcome-based reinforcement learning enables search-augmented language agents to learn from verifiable final answers, but its trajectory-level credit cannot distinguish the contributions of individual actions in a multi-turn search process. We propose EviSD, an evidence-conditioned self-distillation framework that uses instance-level supporting evidence as privileged information for search actions and golden answers as complementary privilege for answer actions. During training, the student samples actions from the original context, while the same model re-scores them as a privileged teacher under an action-aligned context. EviSD converts the detached teacher--student gap into a bounded correction to the outcome-derived GRPO advantage and applies it only to generated action spans. This design localizes privileged guidance while preserving the update direction determined by the outcome reward, without an auxiliary distillation objective or any change at inference time. Across seven question-answering benchmarks and three backbones spanning model scales and generations, EviSD achieves the highest macro-average Exact Match in all evaluated settings, outperforming the strongest compared methods by 1.3--2.3 points while modulating only 6.7%--15.1% of response tokens. Code is available at https://github.com/JiananXie/EviSD.
Search-augmented large language model agents are increasingly capable of solving knowledge-intensive tasks, but their behavior when a multi-hop question is fundamentally unanswerable remains poorly understood. Existing abstention benchmarks largely expose defects at the surface of single-hop queries and therefore cannot reveal failures that emerge only after valid intermediate reasoning and retrieval. We introduce HopRefusalBench, the first controlled benchmark of refusal within multi-hop search, comprising 889 unanswerable questions constructed from KILT-grounded entity paths. It crosses three causes of unanswerability (answer unknown, false premise, and underspecified context) with root, middle, and terminal topologies, making premise verification, intermediate-bridge validation, and terminal stopping separately observable. We further propose a final-outcome taxonomy spanning target-aware refusal, pseudo-refusal, hallucinated completion, and search-budget exhaustion, together with source-aware trajectory metrics for post-trigger continuation and token waste. Across ten frontier proprietary and open-weight models in search-augmented mode, the best model achieves a target-aware correct halting rate (TCHR) of only 42.9%. Root and middle items are consistently harder than terminal items, and all models attain their highest TCHR on false premises and their lowest on underspecified questions. Yet when pooled across categories, 84.7--98.4% of each model's explicit refusal-like responses identify the correct rationale, localizing the main bottleneck to committing to an appropriate non-answer; failed trajectories instead diverge into hallucination or search-budget exhaustion. These results establish refusal in multi-hop search as a consequential evaluation problem and provide a foundation for diagnosing and improving the reliability of search-augmented agents.
Existing search-augmented LLM agents are trained using Reinforcement Learning to boost its reasoning capabilities. However, these approaches primarily rely on outcome-level rewards, which provide little supervision over search behavior and overlook agent's ability to decompose complex queries properly. To mitigate this issue, we propose PROGRESS which utilizes teacher-guided coverage reward to explicitly shape decomposed query generation of the policy model. During training, frozen teacher models are used to decompose complex queries into essential search queries. These essential search queries are utilized to guide the search behavior of the policy model. Integrated into an R1-style training framework, our approach provides lightweight guidance over query decomposition decisions without dense process-level supervision. Experiments show that coverage-guided RL improves overall task performance, highlighting the importance of explicitly supervising search strategies in agentic LLMs.