# SD-Search: On-Policy Hindsight Self-Distillation for Search-Augmented Reasoning

arXiv: https://arxiv.org/abs/2605.18299 · HTML: https://mlsanity.com/paper/2605.18299/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 34 of its 35 references that are in the map.
- First posted on arXiv 18 May 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 34)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Interleaving Retrieval with Chain-of-Thought Reasoning for Knowledge-Intensive Multi-Step Questions](https://mlsanity.com/paper/2212.10509/) (2022)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Search-o1: Agentic Search-Enhanced Large Reasoning Models](https://mlsanity.com/paper/2501.05366/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [ReSearch: Learning to Reason with Search for LLMs via Reinforcement Learning](https://mlsanity.com/paper/2503.19470/) (2025)
- [StepSearch: Igniting LLMs Search Ability via Step-Wise Proximal Policy Optimization](https://mlsanity.com/paper/2505.15107/) (2025)

## Built on by (most cited first, 5 of 5)

- [OPDSearch+: On-Policy Distillation with RL Refinement for Search-Augmented Reasoning](https://mlsanity.com/paper/2608.24310/) (2026)
- [EviSD: Evidence-Conditioned Self-Distillation for Search-Augmented Agents](https://mlsanity.com/paper/2608.01359/) (2026)
- [HindSearch: Trajectory-Level Hindsight Critique for Search-Augmented Reinforcement Learning](https://mlsanity.com/paper/2608.01597/) (2026)
- [IGSD: Environment-Verified Hindsight Self-Distillation for Search Agents](https://mlsanity.com/paper/2609.32694/) (2026)
- [Where the Model Changes Its Mind: Hindsight-Divergence Localization for Efficient Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2609.36864/) (2026)

## Abstract (arXiv)

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 SD-Search, which derives step-level supervision from the policy itself through on-policy 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 the 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 is produced by the policy itself within the standard RL training loop, without external model inference, auxiliary annotation pipeline, or additional training stage.