Abstract-We consider the problem of optimally assigning p sniffers to K channels to monitor the transmission activities in a multi-channel wireless network. The activity of users is initially unknown to the sniffers and is to be learned along with channel assignment decisions while maximizing the benifits of this assignment, resulting in the fundamental trade-off between exploration versus exploitation. We formulate it as the linear partial monitoring problem, a super-class of multi-armed bandits. As the number of arms (sniffer-channel assignments) is exponential, novel techniques are called for, to allow efficient learning. We use the linear bandit model to capture the dependency amongst the arms and develop two policies that take advantage of this dependency. Both policies enjoy logarithmic regret bound of timeslots with a term that is sub-linear in the number of arms.

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