Click efficiency: a unified optimal ranking for online Ads and documents

Ranking of search results and ads has traditionally been studied separately. The probability ranking principle is commonly used to rank the search results while the ranking based on expected profits is commonly used for paid placement of ads. These rankings try to maximize the expected utilities based on the user click models. Recent empirical analysis on search engine logs suggests unified click models for both ranked ads and search results (documents). These new models consider parameters of (i) probability of the user abandoning browsing results (ii) perceived relevance of result snippets. However, current document and ad ranking methods do not consider these parameters. In this paper we propose a generalized ranking function—namely Click Efficiency (CE)—for documents and ads based on empirically proven user click models. The ranking considers parameters (i) and (ii) above, optimal and has the same time complexity as sorting. Furthermore, the CE ranking exploits the commonality of click models, hence is applicable for both documents and ads. We examine the reduced forms of CE ranking based upon different underlying assumptions, enumerating a hierarchy of ranking functions. Interestingly, some of the rankings in the hierarchy are currently used ad and document ranking functions; while others suggest new rankings. Thus, this hierarchy illustrates the relationships between different rankings, and clarifies the underlying assumptions. While optimality of ranking is sufficient for document ranking, applying CE ranking to ad auctions requires an appropriate pricing mechanism. We incorporate a second price based mechanism with the proposed ranking. Our analysis proves several desirable properties including revenue dominance over Vickrey Clarke Groves (VCG) for the same bid vector and existence of a Nash equilibrium in pure strategies. The equilibrium is socially optimal, and revenue equivalent to the truthful VCG equilibrium. As a result of its generality, the auction mechanism and the equilibrium reduces to the current mechanisms including Generalized Second Price Auction (GSP) and corresponding equilibria. Furthermore, we relax the independence assumption in CE ranking and analyze the diversity ranking problem. We show that optimal diversity ranking is NP-Hard in general, and a constant time approximation algorithm is not likely. Finally our simulations to quantify the amount of increase in different utility functions conform to the results, and suggest potentially significant increase in utilities.

[1]  Arpita Ghosh,et al.  Expressive auctions for externalities in online advertising , 2010, WWW '10.

[2]  Erick Cantú-Paz,et al.  Temporal click model for sponsored search , 2010, SIGIR.

[3]  Jon Feldman,et al.  Sponsored Search Auctions with Markovian Users , 2008, WINE.

[4]  Nick Craswell,et al.  An experimental comparison of click position-bias models , 2008, WSDM '08.

[5]  Eric Brill,et al.  Beyond PageRank: machine learning for static ranking , 2006, WWW '06.

[6]  Subbarao Kambhampati,et al.  Optimal Ad-Ranking for Profit Maximization , 2008, WebDB.

[7]  S. Robertson The probability ranking principle in IR , 1997 .

[8]  Mohammad Mahdian,et al.  A Cascade Model for Externalities in Sponsored Search , 2008, WINE.

[9]  E. David,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World , 2010 .

[10]  Ben Carterette,et al.  An analysis of NP-completeness in novelty and diversity ranking , 2009, Information Retrieval.

[11]  Chris Arney,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World (Easley, D. and Kleinberg, J.; 2010) [Book Review] , 2013, IEEE Technology and Society Magazine.

[12]  Michael D. Gordon,et al.  When Is the Probability Ranking Principle Suboptimal? , 1992, J. Am. Soc. Inf. Sci..

[13]  Milad Shokouhi,et al.  Expected browsing utility for web search evaluation , 2010, CIKM.

[14]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[15]  Moshe Tennenholtz,et al.  User modeling in position auctions: re-considering the GSP and VCG mechanisms , 2009, AAMAS.

[16]  Olivier Chapelle,et al.  A dynamic bayesian network click model for web search ranking , 2009, WWW '09.

[17]  Zheng Chen,et al.  A novel click model and its applications to online advertising , 2010, WSDM '10.

[18]  J. Håstad Clique is hard to approximate withinn1−ε , 1999 .

[19]  Benjamin Piwowarski,et al.  A user browsing model to predict search engine click data from past observations. , 2008, SIGIR '08.

[20]  Matthew Richardson,et al.  Predicting clicks: estimating the click-through rate for new ads , 2007, WWW '07.

[21]  Chao Liu,et al.  Click chain model in web search , 2009, WWW '09.

[22]  Charles L. A. Clarke,et al.  The influence of caption features on clickthrough patterns in web search , 2007, SIGIR.

[23]  Johan Håstad,et al.  Clique is hard to approximate within n1-epsilon , 1996, Electron. Colloquium Comput. Complex..

[24]  Sreenivas Gollapudi,et al.  Diversifying search results , 2009, WSDM '09.

[25]  Michael D. Gordon,et al.  A Utility Theoretic Examination of the Probability Ranking Principle in Information Retrieval. , 1991 .

[26]  E. H. Clarke Multipart pricing of public goods , 1971 .

[27]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[28]  Anna R. Karlin,et al.  On the Equilibria and Efficiency of the GSP Mechanism in Keyword Auctions with Externalities , 2008, WINE.

[29]  Ashish Goel,et al.  Truthful auctions for pricing search keywords , 2006, EC '06.

[30]  Xiaotie Deng,et al.  A New Ranking Scheme of the GSP Mechanism with Markovian Users , 2009, WINE.

[31]  Ravi Kumar,et al.  Optimizing two-dimensional search results presentation , 2011, WSDM '11.

[32]  David S. Johnson,et al.  The Complexity of Near-Optimal Graph Coloring , 1976, J. ACM.

[33]  Krishna Bharat,et al.  Diversifying web search results , 2010, WWW '10.

[34]  Michael D. Gordon,et al.  When is the probability ranking principle suboptimal , 1992 .

[35]  Yisong Yue,et al.  Beyond position bias: examining result attractiveness as a source of presentation bias in clickthrough data , 2010, WWW '10.

[36]  Yuchen Zhang,et al.  Characterizing search intent diversity into click models , 2011, WWW.