@inproceedings{zhu-etal-2026-dense,
title = "Dense Process Supervision for Search Agents via Fact Utility Estimation",
author = "Zhu, Rongzhi and
Liu, Xiangyu and
Liu, Yi and
Zhang, Shuo and
Zhang, Ruirui and
Wu, Rui and
Jiang, Tao and
Sun, Zequn and
Xu, Wenhao and
Hu, Wei",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.1050/",
pages = "24115--24130",
ISBN = "979-8-89176-459-0",
abstract = "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."
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<abstract>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.</abstract>
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%0 Conference Proceedings
%T Dense Process Supervision for Search Agents via Fact Utility Estimation
%A Zhu, Rongzhi
%A Liu, Xiangyu
%A Liu, Yi
%A Zhang, Shuo
%A Zhang, Ruirui
%A Wu, Rui
%A Jiang, Tao
%A Sun, Zequn
%A Xu, Wenhao
%A Hu, Wei
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F zhu-etal-2026-dense
%X 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.
%U https://aclanthology.org/2026.emnlp-main.1050/
%P 24115-24130
Markdown (Informal)
[Dense Process Supervision for Search Agents via Fact Utility Estimation](https://aclanthology.org/2026.emnlp-main.1050/) (Zhu et al., EMNLP 2026)
ACL
- Rongzhi Zhu, Xiangyu Liu, Yi Liu, Shuo Zhang, Ruirui Zhang, Rui Wu, Tao Jiang, Zequn Sun, Wenhao Xu, and Wei Hu. 2026. Dense Process Supervision for Search Agents via Fact Utility Estimation. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 24115–24130, Budapest, Hungary. Association for Computational Linguistics.