Bayesian optimization is an effective technique for black-box optimization, but its applicability is typically limited to low-dimensional and small-budget problems due to the cubic complexity of computing the Gaussian process (GP) surrogate. While various approximate GP models have been employed to scale Bayesian optimization to larger sample sizes, most suffer from overly-smooth estimation and focus primarily on problems that allow for large online samples. In this work, we argue that Bayesian optimization algorithms with sparse GPs can more efficiently allocate their representational power to relevant regions of the search space. To achieve this, we propose focalized GP, which leverages a novel variational loss function to achieve stronger local prediction, as well as FocalBO, which hierarchically optimizes the focalized GP acquisition function over progressively smaller search spaces. Experimental results demonstrate that FocalBO can efficiently leverage large amounts of offline and online data to achieve state-of-the-art performance on robot morphology design and to control a 585-dimensional musculoskeletal system.

翻译：贝叶斯优化是黑箱优化的有效技术，但由于计算高斯过程（GP）代理模型具有立方复杂度，其适用性通常局限于低维和小预算问题。尽管已有多种近似GP模型被用于将贝叶斯优化扩展至更大样本规模，但多数方法存在估计过度平滑的问题，且主要关注允许大规模在线采样的问题。本研究中，我们认为采用稀疏GP的贝叶斯优化算法能更高效地将表征能力分配到搜索空间的相关区域。为此，我们提出聚焦GP模型，该模型通过新颖的变分损失函数实现更强的局部预测能力，并在此基础上构建FocalBO算法，该算法在逐步缩小的搜索空间上分层优化聚焦GP的采集函数。实验结果表明，FocalBO能有效利用大量离线和在线数据，在机器人形态设计任务中取得最先进的性能，并成功控制一个585维的肌肉骨骼系统。