Interactively Learning Preference Constraints in Linear Bandits
This work addresses the challenge of efficiently learning expensive-to-evaluate human preference constraints in decision-making systems, such as autonomous driving, with incremental improvements in sample complexity and robustness.
The paper tackles the problem of sequential decision-making with known rewards and unknown constraints, such as human preferences in driving, by formalizing it as a constrained linear best-arm identification problem and proposing the Adaptive Constraint Learning (ACOL) algorithm. The result shows that ACOL's sample complexity matches a lower bound in worst-case scenarios, outperforms baselines in synthetic experiments, and is more sample-efficient and robust in a driving simulation application.
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.