  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.
