  Motivated by problems in search and detection we present a solution to a
Combinatorial Multi-Armed Bandit (CMAB) problem with both heavy-tailed reward
distributions and a new class of feedback, filtered semibandit feedback. In a
CMAB problem an agent pulls a combination of arms from a set $\{1,...,k\}$ in
each round, generating random outcomes from probability distributions
associated with these arms and receiving an overall reward. Under semibandit
feedback it is assumed that the random outcomes generated are all observed.
Filtered semibandit feedback allows the outcomes that are observed to be
sampled from a second distribution conditioned on the initial random outcomes.
This feedback mechanism is valuable as it allows CMAB methods to be applied to
sequential search and detection problems where combinatorial actions are made,
but the true rewards (number of objects of interest appearing in the round) are
not observed, rather a filtered reward (the number of objects the searcher
successfully finds, which must by definition be less than the number that
appear). We present an upper confidence bound type algorithm, Robust-F-CUCB,
and associated regret bound of order $\mathcal{O}(\ln(n))$ to balance
exploration and exploitation in the face of both filtering of reward and heavy
tailed reward distributions.
