We study sequential decision-making with known rewards and unknown constraints, motivated by situations where the constraints represent expensive-to-evaluate human preferences, such as safe and comfortable driving behavior. We formalize the challenge of interactively learning about these constraints as a novel linear bandit problem which we call constrained linear best-arm identification. To solve this problem, we propose the Adaptive Constraint Learning (ACOL) algorithm. We provide an instance-dependent lower bound for constrained linear best-arm identification and show that ACOL's sample complexity matches the lower bound in the worst-case. In the average case, ACOL's sample complexity bound is still significantly tighter than bounds of simpler approaches. In synthetic experiments, ACOL performs on par with an oracle solution and outperforms a range of baselines. As an application, we consider learning constraints to represent human preferences in a driving simulation. ACOL is significantly more sample efficient than alternatives for this application. Further, we find that learning preferences as constraints is more robust to changes in the driving scenario than encoding the preferences directly in the reward function.

探讨了利用Adaptive Constraint Learning算法解决具有昂贵人类偏好未知约束的序列决策问题，特别是在驾驶行为中体现的安全和舒适性约束的识别，该算法在驾驶模拟中比其他算法更加高效

线性贝叶斯中交互学习偏好约束