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.

中文翻译：

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使用蒙特卡罗树搜索学习用于黑盒优化的搜索空间划分

高维黑盒优化具有广泛的应用，但仍然是一个需要解决的具有挑战性的问题。给定一组样本$\{\vx_i, y_i\}$，构建全局模型（如贝叶斯优化（BO））在高维搜索空间中遭受维数诅咒，而贪婪搜索可能导致子- 最优性。通过递归地将搜索空间划分为具有高/低函数值的区域，LaNAS 等近期工作在神经架构搜索 (NAS) 中表现出良好的性能，从经验上降低了样本复杂度。在本文中，我们创造了将 LaNAS 扩展到其他领域的 LA-MCTS。与以前的方法不同，LA-MCTS 以在线方式使用一些样本及其函数值来学习搜索空间的划分。而 LaNAS 使用线性分区并在每个区域进行均匀采样，我们的 LA-MCTS 采用非线性决策边界并学习局部模型来挑选好的候选者。如果非线性分区函数和局部模型与真实黑盒函数很好地拟合，那么可以用更少的样本获得好的分区和候选。LA-MCTS 通过使用现有的黑盒优化器（例如 BO、TuRBO）作为其本地模型，作为 \emph {元算法}，在一般黑盒优化和强化学习基准测试中取得了强大的性能，特别是对于高维问题。