Learning Search Space Partition for Black-box Optimization using Monte Carlo Tree Search

TL;DR

This paper introduces LA-MCTS, a method that learns adaptive, nonlinear partitions of high-dimensional search spaces using Monte Carlo Tree Search, improving black-box optimization efficiency by integrating local models and existing optimizers.

Contribution

LA-MCTS extends previous space partitioning methods by learning nonlinear decision boundaries and incorporating local models, enabling more efficient high-dimensional black-box optimization.

Findings

LA-MCTS outperforms traditional methods in high-dimensional benchmarks.

It reduces sample complexity significantly compared to linear partition approaches.

The method is effective in reinforcement learning tasks with high-dimensional spaces.

Abstract

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.