用树结构建模不确定性，实现黑箱优化的全局搜索。
BARK: A Fully Bayesian Tree Kernel for Black-box Optimization
- 基于贝叶斯加性回归树构建全贝叶斯核函数
- 在合成与真实任务上均优于现有方法
- 能同时量化函数值与树结构的不确定性
我们从高斯过程视角出发，将贝叶斯加性回归树（BART）用于贝叶斯优化。提出的树核方法（BARK）通过树结构的一致性定义分段常数函数的后验分布，并采用马尔可夫链蒙特卡洛方法探索树核空间。与仅采样函数的BART不同，BARK生成定义在函数上的高斯过程样本，可用于构建贝叶斯优化的采集函数。该树基方法可在混合特征空间中实现全局优化。此外，许多已有树核仅对函数值提供不确定性量化，而我们的采样方案还捕捉了树结构本身的不确定性。实验表明，得益于全贝叶斯代理模型与优化流程的结合，BARK在合成与实际基准测试中表现优异。
原文摘要 · Abstract (English)
We perform Bayesian optimization using a Gaussian process perspective on Bayesian Additive Regression Trees (BART). Our BART Kernel (BARK) uses tree agreement to define a posterior over piecewise-constant functions, and we explore the space of tree kernels using a Markov chain Monte Carlo approach. Where BART only samples functions, the resulting BARK model obtains samples of Gaussian processes defining distributions over functions, which allow us to build acquisition functions for Bayesian optimization. Our tree-based approach enables global optimization over the surrogate, even for mixed-feature spaces. Moreover, where many previous tree-based kernels provide uncertainty quantification over function values, our sampling scheme captures uncertainty over the tree structure itself. Our experiments show the strong performance of BARK on both synthetic and applied benchmarks, due to the combination of our fully Bayesian surrogate and the optimization procedure.
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