Noisy Submodular Maximization via Adaptive Sampling with Applications to Crowdsourced Image Collection Summarization

We address the problem of maximizing an unknown submodular function that can only be accessed via noisy evaluations. Our work is motivated by the task of summarizing content, e.g., image collections, by leveraging users' feedback in form of clicks or ratings. For summarization tasks with the goal of maximizing coverage and diversity, submodular set functions are a natural choice. When the underlying submodular function is unknown, users' feedback can provide noisy evaluations of the function that we seek to maximize. We provide a generic algorithm — ExpGreedy — for maximizing an unknown submodular function under cardinality constraints. This algorithm makes use of a novel exploration module— TopX — that proposes good elements based on adaptively sampling noisy function evaluations. TopX is able to accommodate different kinds of observation models such as value queries and pairwise comparisons. We provide PAC-style guarantees on the quality and sampling cost of the solution obtained by ExpGreedy. We demonstrate the effectiveness of our approach in an interactive, crowdsourced image collection summarization application