未知ハイパーパラメータに対するガウス過程の一様誤差上界と安全制約付き制御への応用
Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications
カーネルハイパーパラメータが未知の場合でも、データからハイパーパラメータ空間の信頼領域を構成し、ガウス過程のモデル誤差に対する確率的な一様上界を導出する手法を提案した。学習ベース制御の性能保証にも応用し、従来のガウス過程より優れた上界性能を示した。
著者: Alexandre Capone, Armin Lederer, Sandra Hirche
分類: cs.LG, cs.RO, cs.SY, eess.SY
原文アブストラクト
Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.
