Online Learning of Assignments

Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize value of information? These applications exhibit strong diminishing returns: Selection of redundant ads and information sources decreases their marginal utility. We show that these and other problems can be formalized as repeatedly selecting an assignment of items to positions to maximize a sequence of monotone submodular functions that arrive one by one. We present an efficient algorithm for this general problem and analyze it in the no-regret model.