Online Ranking with Constraints: A Primal-Dual Algorithm and Applications to Web Traffic-Shaping

TL;DR

This paper introduces an online primal-dual algorithm for constrained ranking problems, effectively balancing local user engagement with global business constraints, validated through theoretical guarantees and real web-traffic data experiments.

Contribution

The paper presents a novel primal-dual approach using linear programming duality and the Hungarian algorithm for online constrained ranking, enabling scalable and near-optimal web traffic-shaping solutions.

Findings

The algorithm achieves near-optimal rankings while satisfying global constraints.

The approach is scalable and suitable for real-time web applications.

Theoretical guarantees support the effectiveness of the method.

Abstract

We study the online constrained ranking problem motivated by an application to web-traffic shaping: an online stream of sessions arrive in which, within each session, we are asked to rank items. The challenge involves optimizing the ranking in each session so that local vs. global objectives are controlled: within each session one wishes to maximize a reward (local) while satisfying certain constraints over the entire set of sessions (global). A typical application of this setup is that of page optimization in a web portal. We wish to rank items so that not only is user engagement maximized in each session, but also other business constraints (such as the number of views/clicks delivered to various publishing partners) are satisfied. We describe an online algorithm for performing this optimization. A novel element of our approach is the use of linear programming duality and connections to the celebrated Hungarian algorithm. This framework enables us to determine a set of \emph{shadow prices} for each traffic-shaping constraint that can then be used directly in the final ranking function to assign near-optimal rankings. The (dual) linear program can be solved off-line periodically to determine the prices. At serving time these prices are used as weights to compute weighted rank-scores for the items, and the simplicity of the approach facilitates scalability to web applications. We provide rigorous theoretical guarantees for the performance of our online algorithm and validate our approach using numerical experiments on real web-traffic data from a prominent internet portal.