Best-Arm Identification in Linear Bandits

Marta Soare 1, 2 Alessandro Lazaric 1, 2 Rémi Munos 1, 2
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : 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, we point out the connection to the $G$-optimality criterion used in optimal experimental design.
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Marta Soare, Alessandro Lazaric, Rémi Munos. Best-Arm Identification in Linear Bandits. NIPS - Advances in Neural Information Processing Systems 27, Dec 2014, Montreal, Canada. ⟨hal-01075701⟩

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