  Existing risk-aware multi-armed bandit models typically focus on risk
measures of individual options such as variance. As a result, they cannot be
directly applied to important real-world online decision making problems with
correlated options. In this paper, we propose a novel Continuous
Mean-Covariance Bandit (CMCB) model to explicitly take into account option
correlation. Specifically, in CMCB, there is a learner who sequentially chooses
weight vectors on given options and observes random feedback according to the
decisions. The agent's objective is to achieve the best trade-off between
reward and risk, measured with option covariance. To capture important reward
observation scenarios in practice, we consider three feedback settings, i.e.,
full-information, semi-bandit and full-bandit feedback. We propose novel
algorithms with the optimal regrets (within logarithmic factors), and provide
matching lower bounds to validate their optimalities. Our experimental results
also demonstrate the superiority of the proposed algorithms. To the best of our
knowledge, this is the first work that considers option correlation in
risk-aware bandits and explicitly quantifies how arbitrary covariance
structures impact the learning performance.
