TY - GEN
T1 - Adaptive multiple-arm identification
AU - Chen, Jiecao
AU - Chen, Xi
AU - Zhang, Qin
AU - Zhou, Yuan
N1 - Publisher Copyright:
© 2017 by the author(s).
PY - 2017
Y1 - 2017
N2 - We study the problem of selecting K arms with the highest expected rewards in a stochastic n-armed bandit game. This problem has a wide range of applications, e.g., A/B testing, crowd-sourcing, simulation optimization. Our goal is to develop a PAC algorithm, which, with probability at least 1 - δ, identifies a set of K arms with the aggregate regret at most e. The notion of aggregate regret for multiple-arm identification was first introduced in Zhou et al. (2014), which is defined as the difference of the averaged expected rewards between the selected set of arms and the best K arms. In contrast to Zhou et al. (2014) that only provides instance-independent sample complexity, we introduce a new hardness parameter for characterizing the difficulty of any given instance. We further develop two algorithms and establish the corresponding sample complexity in terms of this hardness parameter. The derived sample complexity can be significantly smaller than state-of-the-art results for a large class of instances and matches the instance-independent lower bound upto a log(e-1) factor in the worst case. We also prove a lower bound result showing that the extra log(ϵ-1) is necessary for instance-dependent algorithms using the introduced hardness parameter.
AB - We study the problem of selecting K arms with the highest expected rewards in a stochastic n-armed bandit game. This problem has a wide range of applications, e.g., A/B testing, crowd-sourcing, simulation optimization. Our goal is to develop a PAC algorithm, which, with probability at least 1 - δ, identifies a set of K arms with the aggregate regret at most e. The notion of aggregate regret for multiple-arm identification was first introduced in Zhou et al. (2014), which is defined as the difference of the averaged expected rewards between the selected set of arms and the best K arms. In contrast to Zhou et al. (2014) that only provides instance-independent sample complexity, we introduce a new hardness parameter for characterizing the difficulty of any given instance. We further develop two algorithms and establish the corresponding sample complexity in terms of this hardness parameter. The derived sample complexity can be significantly smaller than state-of-the-art results for a large class of instances and matches the instance-independent lower bound upto a log(e-1) factor in the worst case. We also prove a lower bound result showing that the extra log(ϵ-1) is necessary for instance-dependent algorithms using the introduced hardness parameter.
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M3 - Conference contribution
AN - SCOPUS:85045580675
T3 - 34th International Conference on Machine Learning, ICML 2017
SP - 1202
EP - 1210
BT - 34th International Conference on Machine Learning, ICML 2017
PB - International Machine Learning Society (IMLS)
T2 - 34th International Conference on Machine Learning, ICML 2017
Y2 - 6 August 2017 through 11 August 2017
ER -