提升多任务贝叶斯优化在不确定相关矩阵下的安全性与灵活性。
Safe Bayesian Optimization for Uncertain Correlation Matrices in Linear Models of Co-Regionalization
- 用线性共区域化模型替代传统模型，更灵活建模任务间相关性。
- 推导出向量函数的统一误差界，保障优化过程的安全性。
- 在基准测试中验证了该方法显著优于传统模型的性能表现。
本文将多任务贝叶斯优化中对不确定共区域化矩阵的安全性保证，从内在共区域化模型扩展至线性共区域化模型。后者通过组合多个特征实现更灵活的任务间相关性建模。我们推导了采用线性共区域化核的高斯过程采样向量函数的统一误差界，并在安全多任务贝叶斯优化基准上进行了数值比较，验证了该模型在性能上的潜在提升。
原文摘要 · Abstract (English)
This paper extends safety guarantees for multi-task Bayesian optimization with uncertain co-regionalization matrices from intrinsic co-regionalization models to linear models of co-regionalization. The latter allows for more flexible modeling of the inter-task correlations by composing multiple features. We derive uniform error bounds for vector-valued functions sampled from a Gaussian process with a linear model of co-regionalization kernel. Furthermore, we show the potential performance gains of linear models of co-regionalization in a numerical comparison on a safe multi-task Bayesian optimization benchmark.
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