# Dense Process Supervision for Search Agents via Fact Utility Estimation

arXiv: https://arxiv.org/abs/2609.00833 · HTML: https://mlsanity.com/paper/2609.00833/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 22 of 22)

- [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)
- [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)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [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)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [BrowseComp: A Simple Yet Challenging Benchmark for Browsing Agents](https://mlsanity.com/paper/2504.12516/) (2025)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [MEM1: Learning to Synergize Memory and Reasoning for Efficient Long-Horizon Agents](https://mlsanity.com/paper/2506.15841/) (2025)
- [ZeroSearch: Incentivize the Search Capability of LLMs without Searching](https://mlsanity.com/paper/2505.04588/) (2025)
- [WebDancer: Towards Autonomous Information Seeking Agency](https://mlsanity.com/paper/2505.22648/) (2025)
- [WebShaper: Agentically Data Synthesizing via Information-Seeking Formalization](https://mlsanity.com/paper/2507.15061/) (2025)
- [MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning](https://mlsanity.com/paper/2402.17231/) (2024)
- [MemSearcher: Training LLMs to Reason, Search and Manage Memory via End-to-End Reinforcement Learning](https://mlsanity.com/paper/2511.02805/) (2025)
- [Mitigating Lost-in-Retrieval Problems in Retrieval Augmented Multi-Hop Question Answering](https://mlsanity.com/paper/2502.14245/) (2025)
- [TURA: Tool-Augmented Unified Retrieval Agent for AI Search](https://mlsanity.com/paper/2508.04604/) (2025)

## Built on by (most cited first, 1 of 1)

- [Pay for the Fault, Not the Flow: Label-Free In-Flow Multi-Agent Workflow Optimization](https://mlsanity.com/paper/2610.01017/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) for search agents typically relies on outcome rewards. However, it often fails to achieve effective credit assignment, due to the unclear value of intermediate steps. It is hard to separate their contributions from the final result. In this paper, we propose a dense process supervision method based on fact utility estimation, which models the reasoning process as the accumulation of discrete evidence facts. We first extract structured facts from raw observations and organize them into an explicit fact store. To support credit assignment, we then cluster semantically equivalent facts and infer the posterior utility of each fact cluster using Bayesian estimation over group rollouts. Finally, we convert the estimated fact utilities into dense step-level rewards to guide RL training. Experiments on seven single-hop and multi-hop QA benchmarks show that our method consistently outperforms existing baselines. Ablation studies validate clear relative improvements on multi-hop QA compared to outcome reward-only training.