Results show that surrogate-guided search can substantially reduce the evaluation cost of gradient-free post-training while producing stronger deployable single experts.
Abstract
Gradient-free post-training has emerged as a compelling alternative to gradient-based optimization for large language models (LLMs), but existing approaches remain costly. We ask whether structured search can identify a strong single expert under a modest evaluation budget. Motivated by evidence that useful weight updates lie in low-dimensional subspaces, we apply Bayesian optimization within a random linear embedding of weight space. Our method requires no backpropagation and uses a Gaussian process surrogate to guide candidate evaluations efficiently. Across several reasoning benchmarks with Qwen2.5-Instruct models from 0.5B to 3B parameters, Bayesian optimization using five times less candidate evaluations matches or exceeds RandOpt. These results show that surrogate-guided search can substantially reduce the evaluation cost of gradient-free post-training while producing stronger deployable single experts.
A unified framework, KENDO (Kernel ENsemble Disagreement-aware Operator), is proposed that integrates Ensemble Gaussian Processes (EGP) with disagreement-aware acquisition strategies and extends the approach to multi-objective optimization via random scalarization that preserves the single-optimizer conditioning structure.
Heng Zhang, Haotian Xiang, Konstantinos D. Polyzos et al.· 0 citations
Gaussian-process Bayesian optimization (GP-BO) excels at black-box optimization of costly functions, e.g., hyperparameter optimization (HPO) and multi-agent system (MAS) design. Convergence-rate guarantees exist for select methods, notably GP upper confidence bound (GP-UCB), but require a fixed kernel. Critically, the kernel encodes how input proximity affects objective value similarity. When raw coordinates poorly match this geometry - as with log-scaled hyperparameters or localized peaks - input warping can greatly improve sample efficiency, yet known GP-UCB proofs require a fixed kernel. We propose Finite-Library Input-Warped Bayesian Optimization (FLIWBO), which selects warps from a finite library of smooth input maps by any history-dependent rule. It adapts the input geometry to accelerate learning while retaining high-probability convergence guarantees under mild hypotheses, with an explicit $\sqrt(N_\varepsilon)$ library-size cost. Controlled diagnostics show that finite-library warping repairs planted geometry mismatches and identify FLIWBO failure cases. Across four repeated benchmarks - warped synthetic objectives, a confidence-fence trap, and Fashion-MNIST HPO - FLIWBO-UCB beats raw-coordinate GP-UCB under misspecified geometry, escapes traps that defeat even oracle-warp expected improvement, and recovers much of the gain from manual log scaling, while leading the tested methods that admit a matching regret guarantee. A 20-dimensional MAS design study further shows feasibility under costly noisy evaluations. Code for experiments is available: https://github.com/edvin-ketabati/bogp-paper-experiments.
Edvin Ketabati Augustinsson, Robert A. Bridges· 0 citations
This work introduces 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, and demonstrates the practical value of agentic BO in dynamic settings.
Paul Brunzema, Louis C. Tiao, Nhat Le et al.· 1 citation
Many design tasks can be cast as black-box function optimization, enabling use of Bayesian optimization to find an ideal design with minimal number of trials. However, often we do not actually need the optimum but instead a sufficiently good solution is enough, for instance a material that is durable enough for its intended use. In most cases there are multiple satisfactory solutions, forming a superlevel set of the function, raising a key question of which one to prefer. We answer this by explaining why robustness to input perturbations that may occur when the solution is deployed is a good criterion and by introduce a Bayesian optimization method that efficiently finds satisficing solutions that are robust to maximally large perturbations. In contrast to previous works, we assume the inputs can be accurately controlled during optimization, but will be perturbed after the deployment.
Samuli Kinnunen, P. Mikkola, Antti Niskanen et al.· arXiv.org· 0 citations
Frontier large language models (LLMs) have become attractive priors for optimization due to their large-scale pretraining that enables them to navigate a variety of optimization settings. However, the effectiveness of modern reasoning LLMs in batch optimization settings remains underexplored. Here we investigate the performance of the current generation of frontier LLMs as batch optimizers in both continuous and discrete settings. We find that while LLMs are competitive zero-shot batch optimizers for numerical test functions, their performance is brittle compared to classical non-LLM optimization approaches. However, LLM priors are significantly better in semantically rich settings, indicating that their batch optimization behavior is highly effective when navigating and reasoning over the discrete spaces most similar in structure to their pretraining data.
Frank Hu, Shriram Chennakesavalu, David Graff· 0 citations
A dual-objective surrogate-guided ensemble search is introduced: candidate architectures are represented as directed acyclic graphs, and two surrogate models are trained independently to estimate predictive accuracy and diversity potential and guide an NES framework that efficiently identifies architectures that are both individually strong and collectively diverse.
Alexandr Udeneev, Petr Babkin, O. Bakhteev· arXiv.org· 0 citations
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