  High dimensional black-box optimization has broad applications but remains a
challenging problem to solve. Given a set of samples $\{\vx_i, y_i\}$, building
a global model (like Bayesian Optimization (BO)) suffers from the curse of
dimensionality in the high-dimensional search space, while a greedy search may
lead to sub-optimality. By recursively splitting the search space into regions
with high/low function values, recent works like LaNAS shows good performance
in Neural Architecture Search (NAS), reducing the sample complexity
empirically. In this paper, we coin LA-MCTS that extends LaNAS to other
domains. Unlike previous approaches, LA-MCTS learns the partition of the search
space using a few samples and their function values in an online fashion. While
LaNAS uses linear partition and performs uniform sampling in each region, our
LA-MCTS adopts a nonlinear decision boundary and learns a local model to pick
good candidates. If the nonlinear partition function and the local model fits
well with ground-truth black-box function, then good partitions and candidates
can be reached with much fewer samples. LA-MCTS serves as a
\emph{meta-algorithm} by using existing black-box optimizers (e.g., BO, TuRBO)
as its local models, achieving strong performance in general black-box
optimization and reinforcement learning benchmarks, in particular for
high-dimensional problems.
