Whole-page optimization and submodular welfare maximization with online bidders

In the context of online ad serving, display ads may appear on different types of web-pages, where each page includes several ad slots and therefore multiple ads can be shown on each page. The set of ads that can be assigned to ad slots of the same page needs to satisfy various pre-specified constraints including exclusion constraints, diversity constraints, and the like. Upon arrival of a user, the ad serving system needs to allocate a set of ads to the current web-page respecting these per-page allocation constraints. Previous slot-based settings ignore the important concept of a page, and may lead to highly suboptimal results in general. In this paper, motivated by these applications in display advertising and inspired by the submodular welfare maximization problem with online bidders, we study a general class of page-based ad allocation problems, present the first (tight) constant-factor approximation algorithms for these problems, and confirm the performance of our algorithms experimentally on real-world data sets. A key technical ingredient of our results is a novel primal-dual analysis for handling free-disposal, which updates dual variables using a "level function" instead of a single level, and unifies with previous analyses of related problems. This new analysis method allows us to handle arbitrarily complicated allocation constraints for each page. Our main result is an algorithm that achieves a 1 -- 1/ε -- o(1) competitive ratio. Moreover, our experiments on real-world data sets show significant improvements of our page-based algorithms compared to the slot-based algorithms. Finally, we observe that our problem is closely related to the submodular welfare maximization (SWM) problem. In particular, we introduce a variant of the SWM problem with online bidders, and show how to solve this problem using our algorithm for whole page optimization.