Multi-objective Good Arm Identification with Bandit Feedback

Code

• github.com/2015211217/MultiThresholdBandit
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Abstract

We consider a good arm identification problem in a stochastic bandit setting with multi-objectives, where each arm i[K] is associated with M distributions D_i^(1), , D_i^(M). For each round t, the player/algorithm pulls one arm i_t and receives a vector feedback, where each component m is sampled according to D_i^(m). The target is twofold, one is finding one arm whose means are larger than the predefined thresholds _1,,_M with a confidence bound and an accuracy rate with a bounded sample complexity, the other is output to indicate no such arm exists. We propose an algorithm with a sample complexity bound. When M=1 and = 0, our bound is the same as the one given in the previous work when and novel bounds for M > 1. The proposed algorithm attains better numerical performance than other baselines in the experiments on synthetic and real datasets.

Reproductions