A data-based online reinforcement learning algorithm satisfying probably approximately correct principle

Abstract

This paper proposes a probably approximately correct (PAC) algorithm that directly utilizes online data efficiently to solve the optimal control problem of continuous deterministic systems without system parameters for the first time. The dependence on some specific approximation structures is crucial to limit the wide application of online reinforcement learning (RL) algorithms. We utilize the online data directly with the kd-tree technique to remove this limitation. Moreover, we design the algorithm in the PAC principle. Complete theoretical proofs are presented, and three examples are simulated to verify its good performance. It draws the conclusion that the proposed RL algorithm specifies the maximum running time to reach a near-optimal control policy with only online data.