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Which ads should we display in sponsored search in order to maximize ourrevenue? How should we dynamically rank information sources to maximize thevalue of the ranking? These applications exhibit strong diminishing returns:Redundancy decreases the marginal utility of each ad or information source. Weshow that these and other problems can be formalized as repeatedly selecting anassignment of items to positions to maximize a sequence of monotone submodularfunctions that arrive one by one. We present an efficient algorithm for thisgeneral problem and analyze it in the no-regret model. Our algorithm possessesstrong theoretical guarantees, such as a performance ratio that converges tothe optimal constant of 1 - 1/e. We empirically evaluate our algorithm on tworeal-world online optimization problems on the web: ad allocation withsubmodular utilities, and dynamically ranking blogs to detect informationcascades. Finally, we present a second algorithm that handles the more generalcase in which the feasible sets are given by a matroid constraint, while stillmaintaining a 1 - 1/e asymptotic performance ratio.

Online Submodular Maximization under a Matroid Constraint with Application to Learning Assignments