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Adaptive Multiple-Arm Identification
Jiecao Chen · Xi Chen · Qin Zhang · Yuan Zhou

Mon Aug 07 01:30 AM -- 05:00 AM (PDT) @ Gallery #125

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, crowdsourcing, simulation optimization. Our goal is to develop a PAC algorithm, which, with probability at least 1-\delta, identifies a set of K arms with the aggregate regret at most \epsilon. 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(\epsilon^{-1}) factor in the worst case. We also prove a lower bound result showing that the extra \log(\epsilon^{-1}) is necessary for instance-dependent algorithms using the introduced hardness parameter.

Author Information

Jiecao (Jack) Chen (Indiana University Bloomington)
Xi Chen (New York University)
Qin Zhang (Indiana University Bloomington)
Yuan Zhou (Indiana University Bloomington)

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