  We present blind exploration and exploitation (BEE) algorithms for
identifying the most reliable stochastic expert based on formulations that
employ posterior sampling, upper-confidence bounds, empirical Kullback-Leibler
divergence, and minmax methods for the stochastic multi-armed bandit problem.
Joint sampling and consultation of experts whose opinions depend on the hidden
and random state of the world becomes challenging in the unsupervised, or
blind, framework as feedback from the true state is not available. We propose
an empirically realizable measure of expert competence that can be inferred
instantaneously using only the opinions of other experts. This measure
preserves the ordering of true competences and thus enables joint sampling and
consultation of stochastic experts based on their opinions on dynamically
changing tasks. Statistics derived from the proposed measure is instantaneously
available allowing both blind exploration-exploitation and unsupervised opinion
aggregation. We discuss how the lack of supervision affects the asymptotic
regret of BEE architectures that rely on UCB1, KL-UCB, MOSS, IMED, and Thompson
sampling. We demonstrate the performance of different BEE algorithms
empirically and compare them to their standard, or supervised, counterparts.
