Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning

Introduction

Active learning techniques are pivotal in scenarios where labeling data is expensive or requires expert intervention. Particularly in engineering and dynamic systems, ensuring that exploration does not violate safety constraints is crucial. Gaussian Processes (GPs) are widely used for this purpose due to their robust uncertainty estimations. However, the traditional method of using Monte-Carlo (MC) sampling for safety evaluation in GPs is computationally intensive, especially for achieving high safety guarantees.

Adaptive Sampling for Safety Evaluation

The authors propose an adaptive sampling method that focuses on the median of the supremum of the posterior GP, which allows for the estimation of safety bounds with fewer samples. This method, termed Adaptive Monte-Carlo (AMC), adjusts the sample size based on online testing, significantly reducing computational costs.

Borell-TIS Inequality for GPs

To further refine the approach, the study employs the Borell-TIS inequality, providing a semi-analytical way to estimate the upper bounds on the safety probability. This method, named Adaptive Borell (AB), combines the strengths of analytical bounds with adaptive sampling, ensuring high precision with minimal computational overhead.

Hybrid Adaptive Scheme

The researchers also introduce a hybrid method (ABM) that combines both adaptive MC sampling and the Borell-TIS bound-based method. This hybrid approach ensures that decisions about the safety of trajectories are made efficiently, making it particularly useful for applications with stringent safety requirements.

Empirical Validation

The proposed methods are validated through simulations and a real-world application involving engine control. The results demonstrate that these approaches enable faster and more efficient active learning by significantly reducing the time needed for safety evaluation. This efficiency allows for more exploration within the same time frame, enhancing learning outcomes.

Conclusion

This study presents a significant advancement in ensuring safety in active learning for dynamic systems. By introducing adaptive sampling methods and leveraging the Borell-TIS inequality, the authors offer a computationally efficient solution for evaluating safety bounds in Gaussian Processes. These developments promise to accelerate active learning tasks without compromising on safety, accuracy, or exploration depth.