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Best-Arm Identification in Linear Bandits
Marta Soare · Alessandro Lazaric · Remi Munos

Wed Dec 10 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D #None
We study the best-arm identification problem in linear bandit, where the rewards of the arms depend linearly on an unknown parameter $\theta^*$ 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.

Author Information

Marta Soare (INRIA Lille - Nord Europe)
Alessandro Lazaric (Facebook Artificial Intelligence Research)
Remi Munos (Google DeepMind)

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