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

Zhixuan Gao; Ke Xue; Rongxi Tan; Ming Chen; Chao Qian

cs.LGSep 28, 2026

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

Authors: Zhixuan Gao, Ke Xue, Rongxi Tan, Ming Chen, Chao Qian

Organizations: State Key Laboratory of Novel Software Technology, Nanjing University · School of Artificial Intelligence, Nanjing University

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.

Figures & tables

Figure 1: Agentic HDBO as an iterative research process. HERA interprets task information, optimization feedback, and structural diagnostics to maintain a revisable working hypothesis. PRISM executes the selected strategy for several evaluations and updates a shared observation history. Outcomes return as evidence for the next round of hypothesis revision.

Aspect	Sara + lenz	HERA + PRISM
Agent role	Experiment designer	Structure strategist
Decision target	Next evaluation point	Structural hypothesis
Candidate generation	LLM or lenz	PRISM only
Control level	Point-level	Strategy-level
Control frequency	Every evaluation	Every search block
Adaptation	Point and BO policy	HDBO strategy

Table 1: Comparison of the primary control roles in Sara with lenz ( Brunzema et al., 2026 ) and our HERA with PRISM.

Tool	Returned information or effect
get_state	Budget and progress, active strategy and scoreboard, geometry, surrogate credibility, structural evidence, and optional metadata/catalog. No state change.
propose_initial_solution	Validate and queue one complete initial design. The next search block evaluates it first.
set_search_strategy	Atomically switch, reconfigure, or restart the numerical strategy without an objective evaluation.
run_search_block	Return every observed value and best-so-far, block improvement, and remaining budget.

Table 2: PRISM tools available to HERA, with arguments validated by PRISM.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Task	$D$	Representation or construction
Hartmann-100	100	Six latent inputs formed by a seeded block-average embedding.
Ackley-200	200	Dense orthogonal mixing over all coordinates; shifted coordinates.
Lévy-300	300	Fifteen block-average latent inputs; shifted coordinates.
Rosenbrock-300	300	Full 300-coordinate chained Rosenbrock; shifted coordinates.
Rover	60	Trajectory-design parameters.
HalfCheetah	102	Continuous-control policy parameters.

Appendix

Table 3: Optimization tasks.

Tool	Contract	Budget
get_state	Inspect a bounded state view. Summary mode reuses compact evidence; full mode refreshes surrogate credibility and structure diagnostics.	None
propose_initial_solution	Propose one prior-informed design after the shared opening design.	One when evaluated
set_search_strategy	Atomically switch, reconfigure, or restart a strategy. Arguments are checked against the selected strategy’s semantic schema.	None
run_search_block	Execute the requested number of sequential proposals, validate every candidate, call the evaluator, and update the shared observation history.	Evaluations returned

Appendix

Table 4: PRISM tools exposed to HERA and their objective-budget effects.

Task	HERA	Full-dimensional BO	TuRBO
Rover	$6.14\pm 2.04$	$84.03\pm 14.23$	$67.64\pm 12.16$
HalfCheetah	$-621.40\pm 370.83$	$-135.37\pm 204.38$	$-166.72\pm 166.04$
MOPTA	$285.57\pm 11.58$	$280.01\pm 3.97$	$286.82\pm 8.52$
Mazda	$-70.73\pm 5.42$	$-73.85\pm 6.88$	$-67.08\pm 5.30$
Ant	$-1105.20\pm 85.48$	$16.85\pm 3.20$	$19.93\pm 3.48$
MM1	$0.8514\pm 0.0224$	$0.8521\pm 0.0152$	$0.8663\pm 0.0271$

Appendix

Table 5: Real-world final objectives: HERA and strong numerical comparators, mean

\pm

sample SD over ten seeds. Lower is better.

Task	Sobol	LLAMBO	Centaur	Sara
Rover	$111.50\pm 6.19$	$27.46\pm 24.94$	$19.64\pm 16.46$	$12.65\pm 0.32$
HC	$-145.60\pm 265.58$	$-415.66\pm 317.55$	$-318.77\pm 199.42$	$-166.03\pm 224.58$
MOPTA	$316.38\pm 5.95$	$325.25\pm 8.63$	$299.84\pm 8.50$	$326.50\pm 8.76$
Mazda	$-46.30\pm 2.63$	$-42.86\pm 7.36$	$-54.17\pm 5.05$	$-47.07\pm 7.27$
Ant	$19.63\pm 1.91$	$-939.50\pm 91.13$	$-1007.07\pm 31.16$	$7.39\pm 23.50$
MM1	$0.8644\pm 0.0130$	$0.8945\pm 0.0140$	$0.8770\pm 0.0164$	$0.8596\pm 0.0238$

Appendix

Table 6: Real-world final objectives for Sobol and LLM/agentic comparators, mean

\pm

sample SD over ten seeds.

Channel	Principal quantities
Exploration geometry	Normalized OTSD, recent OTSD gain, observation entropy, and their trajectories.
Surrogate credibility	Posterior standard-deviation summaries over Sobol probes; held-out RMSE, standardized residuals, $1\sigma/2\sigma$ coverage, and $n/D$ .
Variable sparsity	LassoBO active-set size and fraction, selected coordinates, and a thresholded provisional verdict.
Low-dimensional subspaces	Surrogate-gradient energy dimension and its ratio to $\min(D,M)$ over $M=64$ probe points.
Additive structure	Interaction-graph fragmentation, number and size of candidate groups, linked pairs, and strongest normalized mixed differences.

Appendix

Table 7: HDBO-specific diagnostic state exposed by get_state . All quantities are derived signals for controlling search, not observations of the unknown objective structure.

Model	HalfCheetah	MOPTA	Mazda
DeepSeek-V4.1-Flash	$-621.4\pm 370.8$	$285.57\pm 11.58$	$-70.73\pm 5.42$
Kimi-K3	$-706.0\pm 485.1$	$285.20\pm 9.27$	$-74.51\pm 5.54$
GPT-6-astra	$-323.0\pm 474.2$	$281.72\pm 8.78$	$-75.36\pm 7.23$

Appendix

Table 8: Agent models: mean final objective

\pm

sample SD over ten seeds. The best mean among models differs by task.

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Open paper AskPDF arXiv

Bayesian optimization (BO) has become the standard tool for sample-efficient optimization and owes its efficiency to uncertainty-aware search driven by generic statistical priors. Richer domain priors can improve BO in principle, but encoding them through tailored kernels or problem structure is difficult and rarely done in practice. LLMs can help sidestep this difficulty by making informal priors from natural language, code, and documentation directly available to the optimizer. However, existing LLM-based BO methods either insert the LLM into a fixed role (surrogate, acquisition proxy, or configuration interface) or hand it broad control, sacrificing the systematic exploration that makes BO reliable. We introduce agentic Bayesian optimization: a paradigm in which an LLM agent is the central decision maker in the BO loop while a Bayesian backend provides the uncertainty-aware optimization substrate. The agent configures the problem, queries the backend, selects and commits evaluations, and can revise the optimization strategy during the run by tightening bounds, switching acquisition functions, proposing targeted evaluations, or even reframing the problem following new instructions or observed evidence. We instantiate this idea in Sara, a surrogate-augmented autoresearch agent, and lenz, a modular BoTorch-based backend that the agent can inspect and modify through a structured interface. Across synthetic and real-world benchmarks, Sara preserves the reliability of state-of-the-art BO without prior knowledge, outperforms LLM-based baselines, and uses natural-language priors to improve beyond standard BO. We further demonstrate the practical value of agentic BO in dynamic settings, where Sara reconfigures the full optimization problem on the fly as requirements change, a capability not previously available in standard BO.

Abstract

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