  Motivated by applications in clinical trials and finance, we study the
problem of online convex optimization (with bandit feedback) where the decision
maker is risk-averse. We provide two algorithms to solve this problem. The
first one is a descent-type algorithm which is easy to implement. The second
algorithm, which combines the ellipsoid method and a center point device,
achieves (almost) optimal regret bounds with respect to the number of rounds.
To the best of our knowledge this is the first attempt to address risk-aversion
in the online convex bandit problem.
