Hybrid Models for Mixed Variables in Bayesian Optimization

Hengrui LuoYounghyun ChoJames W. DemmelXiaoye S. LiYang Liu

This paper presents a new type of hybrid models for Bayesian optimization (BO) adept at managing mixed variables, encompassing both quantitative (continuous and integer) and qualitative (categorical) types. Our proposed new hybrid models merge Monte Carlo Tree Search structure (MCTS) for categorical variables with Gaussian Processes (GP) for continuous ones. Addressing efficiency in searching phase, we juxtapose the original (frequentist) upper confidence bound tree search (UCTS) and the Bayesian Dirichlet search strategies, showcasing the tree architecture’s integration into Bayesian optimization. Central to our innovation in surrogate modeling phase is online kernel selection for mixed-variable BO. Our innovations, including dynamic kernel selection, unique UCTS (hybridM) and Bayesian update strategies (hybridD), position our hybrid models as an advancement in mixed-variable surrogate models. Numerical experiments underscore the hybrid models’ superiority, highlighting their potential in Bayesian optimization.

URL: https://arxiv.org/abs/2206.01409