Bayesian optimization techniques have been successfully applied to robotics,
planning, sensor placement, recommendation, advertising, intelligent user
interfaces and automatic algorithm configuration. Despite these successes, the
approach is restricted to problems of moderate dimension, and several workshops
on Bayesian optimization have identified its scaling to high-dimensions as one
of the holy grails of the field. In this paper, we introduce a novel random
embedding idea to attack this problem. The resulting Random EMbedding Bayesian
Optimization (REMBO) algorithm is very simple, has important invariance
properties, and applies to domains with both categorical and continuous
variables. We present a thorough theoretical analysis of REMBO. Empirical
results confirm that REMBO can effectively solve problems with billions of
dimensions, provided the intrinsic dimensionality is low. They also show that
REMBO achieves state-of-the-art performance in optimizing the 47 discrete
parameters of a popular mixed integer linear programming solver.

本文介绍了 Random Embedding Bayesian Optimization (REMBO) 算法，运用随机嵌入思想来攻克高维度问题，此算法简单且具有重要的不变性，应用于具有连续和分类变量的领域，经理论和实证分析证明 REMBO 可在高达数十亿个维度的问题中有效地解决问题，其在优化流行的混合整数线性规划求解器的 47 个离散参数方面也达到了状态的最佳表现。