  Maximising the detection of intrusions is a fundamental and often critical
aim of perimeter surveillance. Commonly, this requires a decision-maker to
optimally allocate multiple searchers to segments of the perimeter. We consider
a scenario where the decision-maker may sequentially update the searchers'
allocation, learning from the observed data to improve decisions over time. In
this work we propose a formal model and solution methods for this sequential
perimeter surveillance problem. Our model is a combinatorial multi-armed bandit
(CMAB) with Poisson rewards and a novel filtered feedback mechanism - arising
from the failure to detect certain intrusions. Our solution method is an upper
confidence bound approach and we derive upper and lower bounds on its expected
performance. We prove that the gap between these bounds is of constant order,
and demonstrate empirically that our approach is more reliable in simulated
problems than competing algorithms.
