  We consider the continuum-armed bandits problem, under a novel setting of
recommending the best arms within a fixed budget under aggregated feedback.
This is motivated by applications where the precise rewards are impossible or
expensive to obtain, while an aggregated reward or feedback, such as the
average over a subset, is available. We constrain the set of reward functions
by assuming that they are from a Gaussian Process and propose the Gaussian
Process Optimistic Optimisation (GPOO) algorithm. We adaptively construct a
tree with nodes as subsets of the arm space, where the feedback is the
aggregated reward of representatives of a node. We propose a new simple regret
notion with respect to aggregated feedback on the recommended arms. We provide
theoretical analysis for the proposed algorithm, and recover single point
feedback as a special case. We illustrate GPOO and compare it with related
algorithms on simulated data.
