Adwords in a Panorama

Three decades ago, Karp, Vazirani, and Vazirani (STOC 1990) defined the online matching problem and gave an optimal 1-frac1e ≈ 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-frac1e 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.