Best-Arm Identification in Linear Bandits
This work addresses sample efficiency in decision-making for linear bandits, which is incremental as it builds on existing methods by incorporating global linear structure.
The paper tackles the best-arm identification problem in linear bandits by characterizing its complexity and introducing sample allocation strategies to minimize the sample budget while ensuring fixed confidence, showing the importance of exploiting linear structure to improve reward estimates for near-optimal arms.
We study the best-arm identification problem in linear bandit, where the rewards of the arms depend linearly on an unknown parameter $θ^*$ and the objective is to return the arm with the largest reward. We characterize the complexity of the problem and introduce sample allocation strategies that pull arms to identify the best arm with a fixed confidence, while minimizing the sample budget. In particular, we show the importance of exploiting the global linear structure to improve the estimate of the reward of near-optimal arms. We analyze the proposed strategies and compare their empirical performance. Finally, as a by-product of our analysis, we point out the connection to the $G$-optimality criterion used in optimal experimental design.