  In this paper, we study an interesting combination of sleeping and
combinatorial stochastic bandits. In the mixed model studied here, at each
discrete time instant, an arbitrary \emph{availability set} is generated from a
fixed set of \emph{base} arms. An algorithm can select a subset of arms from
the \emph{availability set} (sleeping bandits) and receive the corresponding
reward along with semi-bandit feedback (combinatorial bandits).
  We adapt the well-known CUCB algorithm in the sleeping combinatorial bandits
setting and refer to it as \CSUCB. We prove -- under mild smoothness conditions
-- that the \CSUCB\ algorithm achieves an $O(\log (T))$ instance-dependent
regret guarantee. We further prove that (i) when the range of the rewards is
bounded, the regret guarantee of \CSUCB\ algorithm is $O(\sqrt{T \log (T)})$
and (ii) the instance-independent regret is $O(\sqrt[3]{T^2 \log(T)})$ in a
general setting. Our results are quite general and hold under general
environments -- such as non-additive reward functions, volatile arm
availability, a variable number of base-arms to be pulled -- arising in
practical applications. We validate the proven theoretical guarantees through
experiments.
