Online Submodular Maximization under a Matroid Constraint with Application to Learning Assignments
This work addresses online optimization problems with diminishing returns for applications like sponsored search and information ranking, offering a general solution with strong theoretical guarantees.
The paper tackles the problem of online submodular maximization under matroid constraints, such as ad allocation and dynamic ranking, by developing an efficient algorithm with a performance ratio converging to 1 - 1/e, and empirically validates it on real-world web applications.
Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy decreases the marginal utility of each ad or information source. 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. Our algorithm possesses strong theoretical guarantees, such as a performance ratio that converges to the optimal constant of 1 - 1/e. We empirically evaluate our algorithm on two real-world online optimization problems on the web: ad allocation with submodular utilities, and dynamically ranking blogs to detect information cascades. Finally, we present a second algorithm that handles the more general case in which the feasible sets are given by a matroid constraint, while still maintaining a 1 - 1/e asymptotic performance ratio.