Safe Time-Varying Optimization based on Gaussian Processes with Spatio-Temporal Kernel

TL;DR

This paper introduces TVSafeOpt, a Bayesian optimization algorithm with a spatio-temporal kernel, designed to safely optimize unknown, time-varying reward and safety functions in sequential decision-making tasks.

Contribution

The paper presents TVSafeOpt, a novel algorithm that safely tracks time-varying safe regions without explicit change detection, with theoretical guarantees and improved performance over existing methods.

Findings

TVSafeOpt outperforms SafeOpt in safety and optimality on synthetic data.

The algorithm effectively tracks time-varying safe regions without change detection.

Successful application to a gas compressor case study confirms safety in real-world scenarios.

Abstract

Ensuring safety is a key aspect in sequential decision making problems, such as robotics or process control. The complexity of the underlying systems often makes finding the optimal decision challenging, especially when the safety-critical system is time-varying. Overcoming the problem of optimizing an unknown time-varying reward subject to unknown time-varying safety constraints, we propose TVSafeOpt, a new algorithm built on Bayesian optimization with a spatio-temporal kernel. The algorithm is capable of safely tracking a time-varying safe region without the need for explicit change detection. Optimality guarantees are also provided for the algorithm when the optimization problem becomes stationary. We show that TVSafeOpt compares favorably against SafeOpt on synthetic data, both regarding safety and optimality. Evaluation on a realistic case study with gas compressors confirms that TVSafeOpt ensures safety when solving time-varying optimization problems with unknown reward and safety functions.