安全贝叶斯优化中的安全性及其对控制的影响
Safety in safe Bayesian optimization and its ramifications for control
AI总结：
针对SafeOpt类安全贝叶斯优化算法在实际应用中因不确定性界限依赖不可靠启发式及难以界定的再生核希尔伯特空间范数而可能引发安全违规的问题，提出仅依赖已知Lipschitz界限的LoSBO算法及其避免网格化的变体LoS-GP-UCB，以提升控制参数调整的安全性。
摘要：
控制工程中一个反复出现且重要的任务是在约束条件下进行参数调整，这概念上等同于对仅能通过带噪声的评估来访问的黑盒函数进行优化。例如，在控制实践中，预先设计的控制器的参数通常在与被控对象的反馈中在线调整，并且只应尝试安全的参数值，例如避免不稳定性。最近，机器学习方法已被用于这一重要问题，特别是贝叶斯优化（BO）。为了处理安全约束，人们利用了安全BO的算法，尤其是SafeOpt类算法，这些算法在学习型控制、机器人技术及相关领域广受欢迎。然而，我们发现了实际安全性的两个重大障碍。首先，SafeOpt类算法依赖于定量的不确定性界限，而大多数实现将这些界限替换为理论上不支持的启发式方法。其次，理论上有效的不确定性界限关键依赖于一个量——目标函数的再生核希尔伯特空间范数——目前无法使用既定的先验工程知识可靠地界定该量。通过仔细的数值实验，我们表明这些问题确实可能导致安全违规。为了克服这些问题，我们提出了仅依赖已知Lipschitz界限来保证安全性的仅Lipschitz安全贝叶斯优化（LoSBO）算法。此外，我们提出了一种变体（LoS-GP-UCB），它避免了搜索空间的网格化，因此即使对于中等高维问题也适用。
英文摘要：
A recurring and important task in control engineering is parameter tuning under constraints, which conceptually amounts to optimization of a blackbox function accessible only through noisy evaluations. For example, in control practice parameters of a pre-designed controller are often tuned online in feedback with a plant, and only safe parameter values should be tried, avoiding for example instability. Recently, machine learning methods have been deployed for this important problem, in particular, Bayesian optimization (BO). To handle safety constraints, algorithms from safe BO have been utilized, especially SafeOpt-type algorithms, which enjoy considerable popularity in learning-based control, robotics, and adjacent fields. However, we identify two significant obstacles to practical safety. First, SafeOpt-type algorithms rely on quantitative uncertainty bounds, and most implementations replace these by theoretically unsupported heuristics. Second, the theoretically valid uncertainty bounds crucially depend on a quantity - the reproducing kernel Hilbert space norm of the target function - that at present is impossible to reliably bound using established prior engineering knowledge. By careful numerical experiments we show that these issues can indeed cause safety violations. To overcome these problems, we propose Lipschitz-only Safe Bayesian Optimization (LoSBO), a safe BO algorithm that relies only on a known Lipschitz bound for its safety. Furthermore, we propose a variant (LoS-GP-UCB) that avoids gridding of the search space and is therefore applicable even for moderately high-dimensional problems.
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