  We study MNL bandits, which is a variant of the traditional multi-armed
bandit problem, under risk criteria. Unlike the ordinary expected revenue, risk
criteria are more general goals widely used in industries and bussiness. We
design algorithms for a broad class of risk criteria, including but not limited
to the well-known conditional value-at-risk, Sharpe ratio and entropy risk, and
prove that they suffer a near-optimal regret. As a complement, we also conduct
experiments with both synthetic and real data to show the empirical performance
of our proposed algorithms.
