No-Regret Bayesian Optimization with Finite-Library Input-Warped Kernels

2026-09-02

AI Summary

该研究提出了一种有限库输入变形贝叶斯优化(FLIWBO)方法，通过从有限的平滑输入映射库中选择变换来适应输入几何结构，从而提高样本效率并保持高概率收敛保证。

Abstract

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.

Problem

• Gaussian-process Bayesian optimization
• input warping
• convergence guarantees

Innovation

• Finite-Library Input-Warped Bayesian Optimization
• GP-UCB
• Sample Efficiency
• Convergence Guarantees
• Input Warping