Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this purpose. In many technical applications the design space is explored via continuous trajectories, along which the safety needs to be assessed. This is particularly challenging for strict safety requirements in GP methods, as it employs computationally expensive Monte-Carlo sampling of high quantiles. We address these challenges by providing provable safety bounds based on the adaptively sampled median of the supremum of the posterior GP. Our method significantly reduces the number of samples required for estimating high safety probabilities, resulting in faster evaluation without sacrificing accuracy and exploration speed. The effectiveness of our safe active learning approach is demonstrated through extensive simulations and validated using a real-world engine example.

翻译：主动学习物理系统通常必须符合实际安全约束，从而限制了对设计空间的探索。高斯过程及其校准的不确定性估计被广泛用于此目的。在许多技术应用中，设计空间通过连续轨迹进行探索，需要沿这些轨迹评估安全性。这对于高斯过程方法中的严格安全要求尤其具有挑战性，因为它需要采用计算成本高昂的高分位数蒙特卡洛采样。我们通过提供基于后验高斯过程上确界的自适应采样中位数的可证明安全边界来应对这些挑战。我们的方法显著减少了估计高安全概率所需的样本数量，从而在不牺牲精度和探索速度的情况下实现更快的评估。通过大量仿真和真实发动机示例验证，证明了我们安全主动学习方法的有效性。