Adversarial Sleeping Bandit Problems with Multiple Plays: Algorithm and
  Ranking Application
Jianjun Yuan Wei Lee Woon Ludovik Coba
This paper presents an efficient algorithm to solve the sleeping bandit with
multiple plays problem in the context of an online recommendation system. The
problem involves bounded, adversarial loss and unknown i.i.d. distributions for
arm availability. The proposed algorithm extends the sleeping bandit algorithm
for single arm selection and is guaranteed to achieve theoretical performance
with regret upper bounded by $\bigO(kN^2\sqrt{T\log T})$, where $k$ is the
number of arms selected per time step, $N$ is the total number of arms, and $T$
is the time horizon.