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In this work, we propose a method to construct a uniform error bound for the SK predictor. In investigating the asymptotic properties of the proposed uniform error bound, we examine the convergence rate of SK’s predictive variance under the supremum norm in both fixed and random design settings. Our analyses reveal that the large-sample properties of SK prediction depend on the design-point sampling scheme and the budget allocation scheme adopted. Appropriately controlling the order of noise variances through budget allocation is crucial for achieving a desirable convergence rate of SK’s approximation error, as quantified by the uniform error bound, and for maintaining SK’s numerical stability. Moreover, we investigate the impact of noise variance estimation on the uniform error bound’s performance theoretically and numerically. We demonstrate the superiority of the proposed uniform bound to the Bonferroni correction-based simultaneous confidence interval under various experimental settings through numerical evaluations. 

Abstract This paper proposes two sequential metamodel‐based methods for level‐set estimation (LSE) that leverage the uniform bound built on stochastic kriging: predictive variance reduction (PVR) and expected classification improvement (ECI). We show that PVR and ECI possess desirable theoretical performance guarantees and provide closed‐form expressions for their respective sequential sampling criteria to seek the next design point for performing simulation runs, allowing computationally efficient one‐iteration look‐ahead updates. To enhance understanding, we reveal the connection between PVR and ECI's sequential sampling criteria. Additionally, we propose integrating a budget allocation feature with PVR and ECI, which improves computational efficiency and potentially enhances robustness to the impacts of heteroscedasticity. Numerical studies demonstrate the superior performance of the proposed methods compared to state‐of‐the‐art benchmarking approaches when given a fixed simulation budget, highlighting their effectiveness in addressing LSE problems. 

This paper proposes a novel stochastic-skill-level-based shared control framework to assist human novices to emulate human experts in complex dynamic control tasks. The proposed framework aims to infer stochastic-skill-levels (SSLs) of the human novices and provide personalized assistance based on the inferred SSLs. SSL can be assessed as a stochastic variable which denotes the probability that the novice will behave similarly to experts. We propose a data-driven method which can characterize novice demonstrations as a novice model and expert demonstrations as an expert model, respectively. Then, our SSL inference approach utilizes the novice and expert models to assess the SSL of the novices in complex dynamic control tasks. The shared control scheme is designed to dynamically adjust the level of assistance based on the inferred SSL to prevent frustration or tedium during human training due to poorly imposed assistance. The proposed framework is demonstrated by a human subject experiment in a human training scenario for a remotely piloted urban air mobility (UAM) vehicle. The results show that the proposed framework can assess the SSL and tailor the assistance for an individual in real-time. The proposed framework is compared to practice-only training (no assistance) and a baseline shared control approach to test the human learning rates in the designed training scenario with human subjects. A subjective survey is also examined to monitor the user experience of the proposed framework.