Selecting the right tuning parameters for algorithms is a pravelent problem in machine learning that can significantly affect the performance of algorithms. Data-efficient optimization algorithms, such as Bayesian optimization, have been used to automate this process. During experiments on real-world systems such as robotic platforms these methods can evaluate unsafe parameters that lead to safety-critical system failures and can destroy the system. Recently, a safe Bayesian optimization algorithm, called SafeOpt, has been developed, which guarantees that the performance of the system never falls below a critical value; that is, safety is defined based on the performance function. However, coupling performance and safety is often not desirable in practice, since they are often opposing objectives. In this paper, we present a generalized algorithm that allows for multiple safety constraints separate from the objective. Given an initial set of safe parameters, the algorithm maximizes performance but only evaluates parameters that satisfy safety for all constraints with high probability. To this end, it carefully explores the parameter space by exploiting regularity assumptions in terms of a Gaussian process prior. Moreover, we show how context variables can be used to safely transfer knowledge to new situations and tasks. We provide a theoretical analysis and demonstrate that the proposed algorithm enables fast, automatic, and safe optimization of tuning parameters in experiments on a quadrotor vehicle.

为算法选择正确的调整参数是机器学习中的一个常见问题，可以显着影响算法的性能。数据高效的优化算法（例如贝叶斯优化）已用于自动化此过程。在机器人平台等现实系统的实验中，这些方法可以评估导致安全关键系统故障并可能破坏系统的不安全参数。最近，开发了一种安全贝叶斯优化算法，称为 SafeOpt ，它保证系统的性能永远不会低于临界值；也就是说，安全性是根据性能函数来定义的。然而，耦合性能和安全性在实践中通常并不理想，因为它们常常是相反的目标。在本文中，我们提出了一种通用算法，允许与目标分开的多个安全约束。给定一组初始安全参数，该算法可以最大化性能，但仅以高概率评估满足所有约束安全性的参数。为此，它通过利用高斯过程先验的规律性假设来仔细探索参数空间。此外，我们还展示了如何使用上下文变量将知识安全地转移到新的情况和任务。我们提供了理论分析，并证明所提出的算法能够在四旋翼飞行器的实验中快速、自动和安全地优化调整参数。