MOCA-HESP: Meta High-dimensional Bayesian Optimization for Combinatorial and Mixed Spaces via Hyper-ellipsoid Partitioning

TL;DR

This paper introduces MOCA-HESP, a meta high-dimensional Bayesian Optimization method that effectively handles combinatorial and mixed variable spaces using hyper-ellipsoid partitioning and adaptive encoder selection, outperforming existing methods.

Contribution

The paper proposes MOCA-HESP, a novel meta-algorithm for high-dimensional BO in combinatorial and mixed spaces, integrating hyper-ellipsoid partitioning with adaptive encoder selection via multi-armed bandits.

Findings

MOCA-HESP outperforms baseline methods on synthetic benchmarks.

Integrating MOCA-HESP with existing BO optimizers improves their performance.

The method effectively handles high-dimensional, mixed, and combinatorial variable spaces.

Abstract

High-dimensional Bayesian Optimization (BO) has attracted significant attention in recent research. However, existing methods have mainly focused on optimizing in continuous domains, while combinatorial (ordinal and categorical) and mixed domains still remain challenging. In this paper, we first propose MOCA-HESP, a novel high-dimensional BO method for combinatorial and mixed variables. The key idea is to leverage the hyper-ellipsoid space partitioning (HESP) technique with different categorical encoders to work with high-dimensional, combinatorial and mixed spaces, while adaptively selecting the optimal encoders for HESP using a multi-armed bandit technique. Our method, MOCA-HESP, is designed as a \textit{meta-algorithm} such that it can incorporate other combinatorial and mixed BO optimizers to further enhance the optimizers' performance. Finally, we develop three practical BO methods by integrating MOCA-HESP with state-of-the-art BO optimizers for combinatorial and mixed variables: standard BO, CASMOPOLITAN, and Bounce. Our experimental results on various synthetic and real-world benchmarks show that our methods outperform existing baselines. Our code implementation can be found at https://github.com/LamNgo1/moca-hesp