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

TL;DR

This paper introduces efficient algorithms for online submodular maximization under matroid constraints, with strong theoretical guarantees and practical applications in online advertising and information ranking.

Contribution

It presents the first algorithms with provable 1 - 1/e performance ratios for online submodular maximization under matroid constraints, applicable to real-world web problems.

Findings

Algorithms achieve near-optimal performance ratios of 1 - 1/e.

Empirical evaluation on ad allocation and blog ranking demonstrates effectiveness.

Theoretical analysis confirms strong performance guarantees.

Abstract

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.