We address the problem of maximizing an unknownsubmodular function that can only be accessed via noisyevaluations. Our work is motivated by the task of sum-marizing content, e.g., image collections, by leveragingusers’ feedback in form of clicks or ratings. For sum-marization tasks with the goal of maximizing cover-age and diversity, submodular set functions are a nat-ural choice. When the underlying submodular functionis unknown, users’ feedback can provide noisy evalua-tions of the function that we seek to maximize. We pro-vide a generic algorithm – EXPGREEDY– for maximiz-ing an unknown submodular function under cardinalityconstraints. This algorithm makes use of a novel explo-ration module – TOPX – that proposes good elementsbased on adaptively sampling noisy function evalua-tions. TOPX is able to accommodate different kinds ofobservation models such as value queries and pairwisecomparisons. We provide PAC-style guarantees on thequality and sampling cost of the solution obtained byEXPGREEDY. We demonstrate the effectiveness of ourapproach in an interactive, crowdsourced image collec-tion summarization application.

Top