Adwords in a Panorama

TL;DR

This paper introduces a new algorithm for the AdWords problem that surpasses the 0.5-competitive greedy approach, achieving a 0.5016-competitive ratio using innovative techniques like the panorama view and panoramic online correlated selection.

Contribution

It provides the first algorithm for general bids in AdWords with a competitive ratio better than 0.5, advancing the understanding of online matching in advertising.

Findings

Achieved a 0.5016-competitive ratio for AdWords with general bids.

Developed the panorama view formulation for AdWords.

Introduced panoramic online correlated selection technique.

Abstract

Three decades ago, Karp, Vazirani, and Vazirani (STOC 1990) defined the online matching problem and gave an optimal $1-\frac{1}{e} \approx 0.632$-competitive algorithm. Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first generalization called AdWords driven by online advertising and obtained the optimal $1-\frac{1}{e}$ competitive ratio in the special case of small bids. It has been open ever since whether there is an algorithm for general bids better than the $0.5$-competitive greedy algorithm. This paper presents a $0.5016$-competitive algorithm for AdWords, answering this open question on the positive end. The algorithm builds on several ingredients, including a combination of the online primal dual framework and the configuration linear program of matching problems recently explored by Huang and Zhang (STOC 2020), a novel formulation of AdWords which we call the panorama view, and a generalization of the online correlated selection by Fahrbach, Huang, Tao, and Zadimorghaddam (FOCS 2020) which we call the panoramic online correlated selection.