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Pure exploration in multi-armed bandits has emerged as an important frameworkfor modeling decision-making and search under uncertainty. In modernapplications, however, one is often faced with a tremendously large number ofoptions. Even obtaining one observation per option may be too costly renderingtraditional pure exploration algorithms ineffective. Fortunately, one often hasaccess to similar relationships amongst the options that can be leveraged. Inthis paper, we consider the pure exploration problem in stochastic multi-armedbandits where the similarities between the arms are captured by a graph and therewards may be represented as a smooth signal on this graph. In particular, weconsider the problem of finding the arm with the maximum reward (i.e., themaximizing problem) or one with a sufficiently high reward (i.e., thesatisficing problem) under this model. We propose novel algorithms\textbf{\algoname{}} (GRaph-based UcB) and $\zeta$-\textbf{\algoname{}} forthese problems and provide a theoretical characterization of their performancewhich specifically elicits the benefit of the graph side information. We alsoprove a lower bound on the data requirement, showing a large class of problemswhere these algorithms are near-optimal. We complement our theory withexperimental results that show the benefit of capitalizing on such sideinformation.

Maximizing and Satisficing in Multi-armed Bandits with Graph Information