  In this paper, we study the stochastic combinatorial multi-armed bandit
problem under semi-bandit feedback. While much work has been done on algorithms
that optimize the expected reward for linear as well as some general reward
functions, we study a variant of the problem, where the objective is to be
risk-aware. More specifically, we consider the problem of maximizing the
Conditional Value-at-Risk (CVaR), a risk measure that takes into account only
the worst-case rewards. We propose new algorithms that maximize the CVaR of the
rewards obtained from the super arms of the combinatorial bandit for the two
cases of Gaussian and bounded arm rewards. We further analyze these algorithms
and provide regret bounds. We believe that our results provide the first
theoretical insights into combinatorial semi-bandit problems in the risk-aware
case.
