探索する実演者から学ぶ：バンディットにおける最適報酬推定
Learning from an Exploring Demonstrator: Optimal Reward Estimation for Bandits
低後悔の実演者の学習過程、特に探索フェーズを観察してマルチアームバンディットの報酬を推定する「逆バンディット」問題を定式化し、情報理論的下限と最適な推定器を提案した論文。
著者: Wenshuo Guo, Kumar Krishna Agrawal, Aditya Grover, Vidya Muthukumar, Ashwin Pananjady
分類: stat.ML, cs.AI, cs.IT, cs.LG, cs.RO, math.IT
原文アブストラクト
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.
