提出可自适应估计核函数范数的可靠安全优化算法
PACSBO: Probably approximately correct safe Bayesian optimization
- 从数据中自适应估计RKHS范数上界，替代预设值
- 通过局部化范数降低保守性，提升优化效率
- 在仿真与硬件实验中优于现有安全优化方法
安全贝叶斯优化（BO）算法可在不掌握系统动力学的情况下找到最优控制策略，同时以高概率保证安全性。但主流方法需假设函数平滑性：已知再生核希尔伯特空间（RKHS）中某范数的上界。然而，由于RKHS是无限维空间，实践中难以获得未知函数在对应RKHS中的上界。为此，我们提出一种从数据中估计未知函数在RKHS中范数上界的算法，并研究其理论性质。此外，类似基于Lipschitz的方法，我们将RKHS范数视为局部而非全局量，从而减少保守性。将该范数估计与局部解释整合进安全BO算法，得到PACSBO——一种可能近似正确的安全贝叶斯优化算法。我们在数值和硬件实验中验证了其适用性和相对于主流安全BO算法的优势。
原文摘要 · Abstract (English)
Safe Bayesian optimization (BO) algorithms promise to find optimal control policies without knowing the system dynamics while at the same time guaranteeing safety with high probability. In exchange for those guarantees, popular algorithms require a smoothness assumption: a known upper bound on a norm in a reproducing kernel Hilbert space (RKHS). The RKHS is a potentially infinite-dimensional space, and it is unclear how to, in practice, obtain an upper bound of an unknown function in its corresponding RKHS. In response, we propose an algorithm that estimates an upper bound on the RKHS norm of an unknown function from data and investigate its theoretical properties. Moreover, akin to Lipschitz-based methods, we treat the RKHS norm as a local rather than a global object, and thus reduce conservatism. Integrating the RKHS norm estimation and the local interpretation of the RKHS norm into a safe BO algorithm yields PACSBO, an algorithm for probably approximately correct safe Bayesian optimization, for which we provide numerical and hardware experiments that demonstrate its applicability and benefits over popular safe BO algorithms.
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