Computably Continuous Reinforcement-Learning Objectives Are PAC-Learnable

In reinforcement learning, the classic objectives of maximizing discounted and finite-horizon cumulative rewards are PAC-learnable: There algorithms that learn a near-optimal policy with high probability using finite amount samples computation. recent years, researchers have introduced corresponding reinforcement-learning beyond rewards, such as specified linear temporal logic formulas. However, questions about PAC-learnability these new remained open. This work demonstrates general through sufficient conditions for in two analysis settings. particular, considers only sample complexity, we prove if an objective given oracle is uniformly continuous, then it PAC-learnable. Further, computational computable, other words, procedure computes successive approximations objective's value, We give three applications our condition on from literature previously unknown Overall, result helps verify existing objectives' PAC-learnability. Also, some studied not continuous been shown to be PAC-learnable, results could guide design PAC-learnable objectives.