# BED-LLM: Intelligent Information Gathering with LLMs and Bayesian Experimental Design

arXiv: https://arxiv.org/abs/2508.21184 · HTML: https://mlsanity.com/paper/2508.21184/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 77 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## Builds on (most cited first, 30 of 54)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studies](https://mlsanity.com/paper/2208.10264/) (2022)
- [LLMs Get Lost In Multi-Turn Conversation](https://mlsanity.com/paper/2505.06120/) (2025)
- [JudgeLM: Fine-tuned Large Language Models are Scalable Judges](https://mlsanity.com/paper/2310.17631/) (2023)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [CollabLLM: From Passive Responders to Active Collaborators](https://mlsanity.com/paper/2502.00640/) (2025)
- [MaxMin-RLHF: Alignment with Diverse Human Preferences](https://mlsanity.com/paper/2402.08925/) (2024)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [STaR-GATE: Teaching Language Models to Ask Clarifying Questions](https://mlsanity.com/paper/2403.19154/) (2024)
- [Eliciting Human Preferences with Language Models](https://mlsanity.com/paper/2310.11589/) (2023)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Modeling Future Conversation Turns to Teach LLMs to Ask Clarifying Questions](https://mlsanity.com/paper/2410.13788/) (2024)
- [QuestBench: Can LLMs ask the right question to acquire information in reasoning tasks?](https://mlsanity.com/paper/2503.22674/) (2025)
- [Prediction-Oriented Bayesian Active Learning](https://mlsanity.com/paper/2304.08151/) (2023)
- [Beyond Single-Turn: A Survey on Multi-Turn Interactions with Large Language Models](https://mlsanity.com/paper/2504.04717/) (2025)
- [Robin: A multi-agent system for automating scientific discovery](https://mlsanity.com/paper/2505.13400/) (2025)
- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective](https://mlsanity.com/paper/2406.00793/) (2024)

## Built on by (most cited first, 24 of 24)

- [The Dialogue That Heals: A Comprehensive Evaluation of Doctor Agents' Inquiry Capability](https://mlsanity.com/paper/2509.24958/) (2025)
- [Uncertainty-Aware Clarification in LLM Agents with Information Gain](https://mlsanity.com/paper/2606.03135/) (2026)
- [Model Discovery Agent: LLM-assisted Bayesian experiment design for data-efficient discovery of mechanistic world models](https://mlsanity.com/paper/2608.09696/) (2026)
- [LLMs are not (consistently) Bayesian: Quantifying internal (in)consistencies of LLMs' probabilistic beliefs](https://mlsanity.com/paper/2605.06915/) (2026)
- [Uncertainty Propagation in LLM-Based Systems](https://mlsanity.com/paper/2604.23505/) (2026)
- [The Perceptual Bandwidth Bottleneck in Vision-Language Models: Active Visual Reasoning via Sequential Experimental Design](https://mlsanity.com/paper/2605.01345/) (2026)
- [Ask When It Pays: Cost-Aware Open-Ended Interaction for Instance Goal Navigation](https://mlsanity.com/paper/2606.03175/) (2026)
- [Likelihood Hacking in Probabilistic Program Synthesis](https://mlsanity.com/paper/2603.24126/) (2026)
- [MaD Physics: Evaluating information seeking under constraints in physical environments](https://mlsanity.com/paper/2605.10820/) (2026)
- [Ask Now, Use Later: Benchmarking the Proactivity Gap in Long-Lived LLM Agents](https://mlsanity.com/paper/2605.28108/) (2026)
- [Amortising Bayesian Experimental Design for Sequential Information Gathering in LLMs](https://mlsanity.com/paper/2607.03426/) (2026)
- [Game of Thought: Robust Information Seeking with Large Language Models Using Game Theory](https://mlsanity.com/paper/2602.01708/) (2026)
- [Planning to Explore: Curiosity-Driven Planning for LLM Test Generation](https://mlsanity.com/paper/2604.05159/) (2026)
- [What Makes a Good Response? An Empirical Analysis of Quality in Qualitative Interviews](https://mlsanity.com/paper/2604.05163/) (2026)
- [Bayesian control for coding agents](https://mlsanity.com/paper/2606.24453/) (2026)
- [Beyond the Resum'e: A Rubric-Aware Automatic Interview System for Information Elicitation](https://mlsanity.com/paper/2603.01775/) (2026)
- [Uncertainty as a Planning Signal: Multi-Turn Decision Making for Goal-Oriented Conversation](https://mlsanity.com/paper/2604.03924/) (2026)
- [A Proactive Multi-Agent Dialogue Framework for Assessing Social Language Disorder Traits in Autism](https://mlsanity.com/paper/2605.22993/) (2026)
- [RevengeBench: Reverse Engineering Code-Space Policies from Behavioral Experiments](https://mlsanity.com/paper/2606.26094/) (2026)
- [Active Inference as Context Acquisition for AI Agents](https://mlsanity.com/paper/2608.19202/) (2026)
- [From Uncertainty to Clinical Risk: Severity-Aware Conformal Planning for Interactive Medical Diagnosis](https://mlsanity.com/paper/2608.27847/) (2026)
- [GUIDE: Generative Utility Inference and Decision Engine](https://mlsanity.com/paper/2609.12137/) (2026)
- [Verbalized and Internal Probabilities Are Coupled in Large Language Models](https://mlsanity.com/paper/2610.00827/) (2026)
- [Explore, Then Commit: Measurement-Efficient Scientific Law Discovery with Language Models](https://mlsanity.com/paper/2610.07620/) (2026)

## Abstract (arXiv)

We propose a general-purpose approach for improving the ability of large language models (LLMs) to intelligently and adaptively gather information from a user or other external source using the framework of sequential Bayesian experimental design (BED). This enables LLMs to act as effective multi-turn conversational agents and interactively interface with external environments. Our approach, which we call BED-LLM (Bayesian experimental design with large language models), is based on iteratively choosing questions or queries that maximize the expected information gain (EIG) with respect to a variable of interest given the responses gathered previously. We show how this EIG can be formulated (and then estimated) in a principled way using a probabilistic model derived from the LLM's predictive distributions and provide detailed insights into key decisions in its construction and updating procedure. We find that BED-LLM achieves substantial gains in performance across a wide range of tests based on the 20 Questions game and using the LLM to actively infer user preferences, compared to purely prompting-based design generation and other adaptive design strategies.