  We consider stochastic sequential learning problems where the learner can
observe the \textit{average reward of several actions}. Such a setting is
interesting in many applications involving monitoring and surveillance, where
the set of the actions to observe represent some (geographical) area. The
importance of this setting is that in these applications, it is actually
\textit{cheaper} to observe average reward of a group of actions rather than
the reward of a single action. We show that when the reward is \textit{smooth}
over a given graph representing the neighboring actions, we can maximize the
cumulative reward of learning while \textit{minimizing the sensing cost}. In
this paper we propose CheapUCB, an algorithm that matches the regret guarantees
of the known algorithms for this setting and at the same time guarantees a
linear cost again over them. As a by-product of our analysis, we establish a
$\Omega(\sqrt{dT})$ lower bound on the cumulative regret of spectral bandits
for a class of graphs with effective dimension $d$.
