Agentic High-Dimensional Bayesian Optimization with Hypothesis- and Evidence-Guided Search

2026-09-28

AI Summary

This study addresses the challenge of ineffective strategy selection in high-dimensional Bayesian optimization (HDBO) arising from unknown problem structures. To this end, we propose HERA, an intelligent agent framework that adopts a hypothesis-evidence guided paradigm to dynamically revise modeling assumptions and configure HDBO strategies by leveraging task context and structural diagnostics. By integrating a PRISM engine for intra-block candidate generation and adaptive model updating, HERA overcomes the reliability bottlenecks of conventional large language models in high-dimensional spaces. Experimental results demonstrate that the proposed approach consistently outperforms existing methods on both synthetic and real-world benchmark tasks. Furthermore, its adaptive mechanism significantly reduces inference costs, highlighting the framework’s efficiency and practicality for complex optimization problems.

Abstract

High-dimensional Bayesian optimization (HDBO) seeks sample-efficient optimization when the number of variables is large relative to the evaluation budget. Recent LLM-based and agentic BO methods incorporate task knowledge and adapt search decisions during a run, but have primarily been evaluated on low- and moderate-dimensional problems. We ask whether this paradigm can transfer to the higher-dimensional regime. Our experiments show that these methods do not remain reliable in the high-dimensional regime, where the challenge is not only where to evaluate, but also which modeling assumption and search geometry to use when the objective's useful structure is unknown. We therefore introduce HERA, a Hypothesis- and Evidence-guided Research Agent that uses task context, optimization feedback, and structural diagnostics to revise search hypotheses, select and configure HDBO strategies, and determine their execution length. PRISM, its numerical optimization engine, generates and evaluates candidates sequentially within each search block, updating numerical models after each observation. HERA remains competitive with strong numerical HDBO baselines and outperforms the evaluated LLM-based and agentic methods on four metadata-free synthetic functions. Across eight real-world tasks, HERA achieves the best mean final objective among all evaluated systems on most benchmarks. Further analyses show that structural diagnostics change strategy use, metadata effects vary across tasks, and adaptive search blocks reduce inference cost.

Problem

• High-dimensional Bayesian optimization
• Agentic search
• Large language models
• Sample-efficient optimization

Innovation

• High-Dimensional Bayesian Optimization
• Agentic Search
• Hypothesis- and Evidence-Guided Agent
• Structural Diagnostics
• Adaptive Search Blocks