用聚焦稀疏高斯过程提升贝叶斯优化效率，适合大规模高维问题。
Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes
- 提出聚焦稀疏高斯过程，通过新变分损失增强局部预测能力。
- 在585维肌骨骼系统控制中表现最优，可高效利用大量离线和在线数据。
- 适合需要高维、大规模数据的机器人设计与复杂系统优化场景。
贝叶斯优化是黑箱优化的有效方法，但通常受限于低维和小样本，因其高斯过程代理模型存在立方复杂度。尽管已有多种近似高斯过程模型用于扩展贝叶斯优化，多数仍存在过度平滑估计的问题，且主要针对支持大量在线采样的任务。本文认为，采用稀疏高斯过程的贝叶斯优化算法能更高效地将表示能力集中于搜索空间的相关区域。为此，我们提出聚焦稀疏高斯过程（focalized GP），利用新颖的变分损失函数实现更强的局部预测能力，并提出FocalBO，通过逐层缩小搜索空间来层次化优化聚焦稀疏高斯过程的采集函数。实验表明，FocalBO能高效利用大量离线与在线数据，在机器人形态设计和585维肌骨骼系统控制任务上达到当前最优性能。
原文摘要 · Abstract (English)
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.
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