Stagewise Safe Bayesian Optimization with Gaussian Processes
This work addresses safety-critical optimization problems in domains like medical therapy and robotic control, offering a novel algorithmic approach with incremental improvements over prior methods.
The paper tackles the problem of optimizing an unknown utility function under unknown safety constraints in sequential decision-making, introducing StageOpt, a safe Bayesian optimization algorithm that separates safe region expansion and utility maximization into distinct stages. It demonstrates that StageOpt is more efficient and broadly applicable than existing methods, with theoretical safety and convergence guarantees, and shows effectiveness in synthetic experiments and clinical spinal cord stimulation therapy optimization.
Enforcing safety is a key aspect of many problems pertaining to sequential decision making under uncertainty, which require the decisions made at every step to be both informative of the optimal decision and also safe. For example, we value both efficacy and comfort in medical therapy, and efficiency and safety in robotic control. We consider this problem of optimizing an unknown utility function with absolute feedback or preference feedback subject to unknown safety constraints. We develop an efficient safe Bayesian optimization algorithm, StageOpt, that separates safe region expansion and utility function maximization into two distinct stages. Compared to existing approaches which interleave between expansion and optimization, we show that StageOpt is more efficient and naturally applicable to a broader class of problems. We provide theoretical guarantees for both the satisfaction of safety constraints as well as convergence to the optimal utility value. We evaluate StageOpt on both a variety of synthetic experiments, as well as in clinical practice. We demonstrate that StageOpt is more effective than existing safe optimization approaches, and is able to safely and effectively optimize spinal cord stimulation therapy in our clinical experiments.