Learning Algorithms for Second-Price Auctions with Reserve

Second-price auctions with reserve play a critical role in the revenue of modern search engine and popular online sites since the revenue of these companies often directly depends on the outcome of such auctions. The choice of the reserve price is the main mechanism through which the auction revenue can be influenced in these electronic markets. We cast the problem of selecting the reserve price to optimize revenue as a learning problem and present a full theoretical analysis dealing with the complex properties of the corresponding loss function. We further give novel algorithms for solving this problem and report the results of several experiments in both synthetic and real-world data demonstrating their effectiveness.

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

[2]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[3]  David M. Pennock,et al.  Revenue analysis of a family of ranking rules for keyword auctions , 2007, EC '07.

[4]  S. Muthukrishnan,et al.  Ad Exchanges: Research Issues , 2009, WINE.

[5]  Jian Hu,et al.  Optimizing search engine revenue in sponsored search , 2009, SIGIR.

[6]  Anton Schwaighofer,et al.  Budget Optimization for Sponsored Search: Censored Learning in MDPs , 2012, UAI.

[7]  I. E. Yen On Convergence Rate of Concave-Convex Procedure , 2012 .

[8]  Umar Syed,et al.  Learning Prices for Repeated Auctions with Strategic Buyers , 2013, NIPS.

[9]  Di He,et al.  Online learning for auction mechanism in bandit setting , 2013, Decis. Support Syst..

[10]  Gert R. G. Lanckriet,et al.  A Proof of Convergence of the Concave-Convex Procedure Using Zangwill's Theory , 2012, Neural Computation.

[11]  Vijay Kumar,et al.  Online learning in online auctions , 2003, SODA '03.

[12]  Ameet Talwalkar,et al.  Foundations of Machine Learning , 2012, Adaptive computation and machine learning.

[13]  Claudio Gentile,et al.  Regret Minimization for Reserve Prices in Second-Price Auctions , 2013, IEEE Transactions on Information Theory.

[14]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[15]  T. P. Dinh,et al.  Convex analysis approach to d.c. programming: Theory, Algorithm and Applications , 1997 .

[16]  D. Pollard Convergence of stochastic processes , 1984 .

[17]  Le Thi Hoai An,et al.  A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem , 1998, SIAM J. Optim..

[18]  Hoang Tuy,et al.  Counter-Examples to Some Results on D . C . Optimization , 2003 .

[19]  Mehryar Mohri,et al.  Non-parametric Revenue Optimization for Generalized Second Price auctions , 2015, UAI.

[20]  Tjalling C. Koopmans,et al.  Additively decomposed quasiconvex functions , 1982, Math. Program..

[21]  Wei Li,et al.  Bid landscape forecasting in online ad exchange marketplace , 2011, KDD.

[22]  John Langford,et al.  Maintaining Equilibria During Exploration in Sponsored Search Auctions , 2010, Algorithmica.

[23]  Peter Auer,et al.  The Nonstochastic Multiarmed Bandit Problem , 2002, SIAM J. Comput..

[24]  R. Horst,et al.  DC Programming: Overview , 1999 .

[25]  M. Talagrand,et al.  Probability in Banach spaces , 1991 .

[26]  Jon M. Kleinberg,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World [Book Review] , 2013, IEEE Technol. Soc. Mag..

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

[28]  Paul R. Milgrom,et al.  A theory of auctions and competitive bidding , 1982 .

[29]  Alan L. Yuille,et al.  The Concave-Convex Procedure , 2003, Neural Computation.

[30]  Frank Thomson Leighton,et al.  The value of knowing a demand curve: bounds on regret for online posted-price auctions , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[31]  Maria-Florina Balcan,et al.  Reducing mechanism design to algorithm design via machine learning , 2007, J. Comput. Syst. Sci..

[32]  Nikhil R. Devanur,et al.  The price of truthfulness for pay-per-click auctions , 2009, EC '09.

[33]  Michael Ostrovsky,et al.  Reserve Prices in Internet Advertising Auctions: A Field Experiment , 2009, Journal of Political Economy.

[34]  Michael I. Jordan,et al.  Convexity, Classification, and Risk Bounds , 2006 .

[35]  V. Koltchinskii,et al.  Empirical margin distributions and bounding the generalization error of combined classifiers , 2002, math/0405343.

[36]  A. Rusakov Concave programming under simplest linear constraints , 2003 .