Online Stochastic Packing Applied to Display Ad Allocation

TL;DR

This paper introduces a near-optimal online algorithm for stochastic packing linear programs, improving approximation guarantees for resource allocation problems, and evaluates its effectiveness on real display ad data.

Contribution

It presents a primal-dual training-based algorithm achieving near-optimal approximation in stochastic models and demonstrates its practical effectiveness on real ad allocation data.

Findings

The algorithm achieves a (1 - o(1))-approximation in the stochastic model.

Training-based algorithms perform well on real display ad data.

There is a trade-off between fairness and efficiency in ad allocation.

Abstract

Inspired by online ad allocation, we study online stochastic packing linear programs from theoretical and practical standpoints. We first present a near-optimal online algorithm for a general class of packing linear programs which model various online resource allocation problems including online variants of routing, ad allocations, generalized assignment, and combinatorial auctions. As our main theoretical result, we prove that a simple primal-dual training-based algorithm achieves a (1 - o(1))-approximation guarantee in the random order stochastic model. This is a significant improvement over logarithmic or constant-factor approximations for the adversarial variants of the same problems (e.g. factor 1 - 1/e for online ad allocation, and \log m for online routing). We then focus on the online display ad allocation problem and study the efficiency and fairness of various training-based and online allocation algorithms on data sets collected from real-life display ad allocation system. Our experimental evaluation confirms the effectiveness of training-based primal-dual algorithms on real data sets, and also indicate an intrinsic trade-off between fairness and efficiency.