Learning from an Exploring Demonstrator: Optimal Reward Estimation for Bandits
This addresses a fundamental problem in reinforcement learning for researchers and practitioners by enabling reward estimation from suboptimal demonstrations, which is incremental but improves upon existing methods.
The paper tackles the problem of estimating rewards in multi-armed bandits by observing a low-regret demonstrator's learning process, overcoming identifiability issues in inverse reinforcement learning, and shows that consistent reward estimation is possible with optimal tradeoffs between estimation and exploration.
We introduce the "inverse bandit" problem of estimating the rewards of a multi-armed bandit instance from observing the learning process of a low-regret demonstrator. Existing approaches to the related problem of inverse reinforcement learning assume the execution of an optimal policy, and thereby suffer from an identifiability issue. In contrast, we propose to leverage the demonstrator's behavior en route to optimality, and in particular, the exploration phase, for reward estimation. We begin by establishing a general information-theoretic lower bound under this paradigm that applies to any demonstrator algorithm, which characterizes a fundamental tradeoff between reward estimation and the amount of exploration of the demonstrator. Then, we develop simple and efficient reward estimators for upper-confidence-based demonstrator algorithms that attain the optimal tradeoff, showing in particular that consistent reward estimation -- free of identifiability issues -- is possible under our paradigm. Extensive simulations on both synthetic and semi-synthetic data corroborate our theoretical results.