Gaussian Process Classification Bandits

Classification bandits are multi-armed bandit problems whose task is to classify a given set of arms into either positive or negative class depending on whether the rate of the arms with the expected reward of at least h is not less than w for given thresholds h and w. We study a special classification bandit problem in which arms correspond to points x in d-dimensional real space with expected rewards f(x) which are generated according to a Gaussian process prior. We develop a framework algorithm for the problem using various arm selection policies and propose policies called FCB and FTSV. We show a smaller sample complexity upper bound for FCB than that for the existing algorithm of the level set estimation, in which whether f(x) is at least h or not must be decided for every arm's x. Arm selection policies depending on an estimated rate of arms with rewards of at least h are also proposed and shown to improve empirical sample complexity. According to our experimental results, the rate-estimation versions of FCB and FTSV, together with that of the popular active learning policy that selects the point with the maximum variance, outperform other policies for synthetic functions, and the version of FTSV is also the best performer for our real-world dataset.

A Bad Arm Existence Checking Problem

We study a bad arm existing checking problem in which a player's task is to judge whether a positive arm exists or not among given K arms by drawing as small number of arms as possible. Here, an arm is positive if its expected loss suffered by drawing the arm is at least a given threshold. This problem is a formalization of diagnosis of disease or machine failure. An interesting structure of this problem is the asymmetry of positive and negative (non-positive) arms' roles; finding one positive arm is enough to judge existence while all the arms must be discriminated as negative to judge non-existence. We propose an algorithms with arm selection policy (policy to determine the next arm to draw) and stopping condition (condition to stop drawing arms) utilizing this asymmetric problem structure and prove its effectiveness theoretically and empirically.