Multistage comparative PAC learning and control

Abstract

In this paper, we develop adaptive PAC (probably approximately correct) learning methods with applications to design control strategy for uncertain systems. The proposed PAC learning methods mimic the adaptive learning behavior of human being to accumulate evidence step by step and make decisions based on available observations. In the proposed methods, new comparative inferential techniques are developed to quickly eliminate inferior hypotheses. We demonstrate that the proposed PAC learning methods are substantially more efficient in finding the optimal hypothesis with pre-specified level of confidence and accuracy. The proposed PAC learning methods can be applied to the design of robust controllers, where the uncertain parameters of the relevant system is sampled to obtain training examples for the learning process.