  In this paper, we study censored Semi-Bandits, a novel variant of the
semi-bandits problem. The learner is assumed to have a fixed amount of
resources, which it allocates to the arms at each time step. The loss observed
from an arm is random and depends on the amount of resources allocated to it.
More specifically, the loss equals zero if the allocation for the arm exceeds a
constant (but unknown)threshold that can be dependent on the arm. Our goal is
to learn a feasible allocation that minimizes the expected loss. The problem is
challenging because the loss distribution and threshold value of each arm are
unknown. We study this novel setting by establishing its `equivalence' to
Multiple-Play Multi-Armed Bandits(MP-MAB) and Combinatorial Semi-Bandits.
Exploiting these equivalences, we derive optimal algorithms for our setting
using existing algorithms for MP-MABand Combinatorial Semi-Bandits. Experiments
on synthetically generated data validate performance guarantees of the proposed
algorithms.
