Monte Carlo Tree Search based Variable Selection for High Dimensional Bayesian Optimization
About
Bayesian optimization (BO) is a class of popular methods for expensive black-box optimization, and has been widely applied to many scenarios. However, BO suffers from the curse of dimensionality, and scaling it to high-dimensional problems is still a challenge. In this paper, we propose a variable selection method MCTS-VS based on Monte Carlo tree search (MCTS), to iteratively select and optimize a subset of variables. That is, MCTS-VS constructs a low-dimensional subspace via MCTS and optimizes in the subspace with any BO algorithm. We give a theoretical analysis of the general variable selection method to reveal how it can work. Experiments on high-dimensional synthetic functions and real-world problems (i.e., NAS-bench problems and MuJoCo locomotion tasks) show that MCTS-VS equipped with a proper BO optimizer can achieve state-of-the-art performance.
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Black-box Optimization | Hartmann-6D 300 evaluations | Wall Clock Time (s)3.711 | 10 | |
| Black-box Optimization | Hartmann-6D 500 evaluations | Wall Clock Time (s)4.59 | 10 | |
| Black-box Optimization | Levy-10D 100 evaluations | Wall Clock Time (s)2.683 | 8 | |
| Black-box Optimization | Levy-10D 300 evaluations | Wall Clock Time (s)3.753 | 8 | |
| Synthetic Function Optimization | Levy-10D 100 evaluations | Mean Objective Value-2.62 | 4 | |
| Synthetic Function Optimization | Levy-10D 300 evaluations | Mean Objective Value-1.765 | 4 | |
| Synthetic Function Optimization | Hartmann 300 evaluations 6D | Mean Objective Value3.153 | 4 | |
| Synthetic Function Optimization | Hartmann-6D 500 evaluations | Mean Objective Value3.012 | 4 |