Simultaneously Learning and Optimizing Using Controlled Variance Pricing

References

• Aghion P, Bolton P, Harris C, Jullien B (1991) Optimal learning by experimentation. Rev. Econom. Stud. 58(4):621–654.Crossref, Google Scholar
• Anderson TW, Taylor JB (1976) Some experimental results on the statistical properties of least squares estimates in control problems. Econometrica 44(6):1289–1302.Crossref, Google Scholar
• Araman VF, Caldentey R (2009) Dynamic pricing for nonperishable products with demand learning. Oper. Res. 57(5):1169–1188.Link, Google Scholar
• Balvers RJ, Cosimano TF (1990) Actively learning about demand and the dynamics of price adjustment. Econom. J. 100(402):882–898.Google Scholar
• Bartlett MS (1951) An inverse matrix adjustment arising in discriminant analysis. Ann. Math. Statist. 22(1):107–111.Crossref, Google Scholar
• Bertsimas D, Perakis G (2006) Dynamic pricing: A learning approach. Hearn D, Lawphongpanich S, eds. Mathematical and Computational Models for Congestion Charging (Springer, New York), 45–79.Crossref, Google Scholar
• Besbes O, Zeevi A (2009) Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms. Oper. Res. 57(6):1407–1420.Link, Google Scholar
• Besbes O, Zeevi A (2011) On the minimax complexity of pricing in a changing environment. Oper. Res. 59(1):66–79.Link, Google Scholar
• Broder J, Rusmevichientong P (2012) Dynamic pricing under a general parametric choice model. Oper. Res. 60(4):965–980.Link, Google Scholar
• Carvalho AX, Puterman ML (2005a) Dynamic optimization and learning: How should a manager set prices when the demand function is unknown? IPEA Discussion Paper 1117. Instituto de Pesquisa Economica Aplicada, Brasilia.Google Scholar
• Carvalho AX, Puterman ML (2005b) Learning and pricing in an Internet environment with binomial demand. J. Revenue Pricing Management 3(4):320–336.Crossref, Google Scholar
• Cesa-Bianchi N, Lugosi G (2006) Prediction, Learning, and Games (Cambridge University Press, New York).Crossref, Google Scholar
• Chen K, Hu I (1998) On consistency of Bayes estimates in a certainty equivalence adaptive system. IEEE Trans. Automatic Control 43(7):943–947.Crossref, Google Scholar
• Chow YS, Teicher H (2003) Probability Theory: Independence, Interchangeability, Martingales, 3rd ed. (Springer Verlag, New York).Google Scholar
• Cope E (2007) Bayesian strategies for dynamic pricing in e-commerce. Naval Res. Logist. 54(3):265–281.Crossref, Google Scholar
• den Boer AV, Zwart B (2012) Mean square convergence rates for maximum quasi-likelihood estimators. Working paper, University of Technology, Eindhoven, The Netherlands. https://www.researchgate.net/publication/257985753_Mean_square_convergence_rates_for_maximum_quasi-likelihood_estimators.Google Scholar
• Duistermaat JJ, Kolk JAC (2004) Multidimensional Real Analysis: Differentiation, Cambridge Studies in Advanced Mathematics, Vol. 86 (Cambridge University Press, Cambridge, UK).Google Scholar
• Easley D, Kiefer NM (1988) Controlling a stochastic process with unknown parameters. Econometrica 56(5):1045–1064.Crossref, Google Scholar
• Eren SS, Maglaras C (2010) Monopoly pricing with limited demand information. J. Revenue Pricing Management 9:23–48.Crossref, Google Scholar
• Farias VF, van Roy B (2010) Dynamic pricing with a prior on market response. Oper. Res. 58(1):16–29.Link, Google Scholar
• Gill J (2001) Generalized Linear Models: A Unified Approach (Sage Publications, Thousand Oaks, CA).Crossref, Google Scholar
• Gittins JC (1989) Multi-Armed Bandit Allocation Indices, Wiley Interscience Series in Systems and Optimization (John Wiley & Sons, New York).Google Scholar
• Godambe VP, Heyde CC (1987) Quasi-likelihood and optimal estimation. Internat. Statist. Rev. 55(3):231–244.Crossref, Google Scholar
• Goldenshluger A, Zeevi A (2009) Woodroofe's one-armed bandit problem revisited. Ann. Appl. Probab. 19(4):1603–1633.Crossref, Google Scholar
• Harrison JM, Keskin NB, Zeevi A (2012) Bayesian dynamic pricing policies: Learning and earning under a binary prior distribution. Management Sci. 58(3):570–586.Link, Google Scholar
• Heyde CC (1997) Quasi-Likelihood and Its Application. Springer Series in Statistics (Springer Verlag, New York).Crossref, Google Scholar
• Keller G, Rady S (1999) Optimal experimentation in a changing environment. Rev. Econom. Stud. 66(3):475–507.Crossref, Google Scholar
• Keskin NB, Zeevi A (2013) Dynamic pricing with an unknown linear demand model: Asymptotically optimal semi-myopic policies. Working paper, University of Chicago Booth School of Business, Chicago. http://faculty.chicagobooth.edu/bora.keskin/pdfs/DynamicPricingUnknownDemandModel.pdf.Google Scholar
• Kiefer J, Wolfowitz J (1952) Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. 23(3):462–466.Crossref, Google Scholar
• Kiefer NM, Nyarko Y (1989) Optimal control of an unknown linear process with learning. Internat. Econom. Rev. 30(3):571–586.Crossref, Google Scholar
• Kleinberg R, Leighton T (2003) The value of knowing a demand curve: Bounds on regret for online posted-price auctions. Proc. 44th IEEE Sympos. Foundations Comput. Sci. (IEEE Computer Society, Washington, DC), 594–605.Crossref, Google Scholar
• Lai TL, Robbins H (1982) Iterated least squares in multiperiod control. Adv. Appl. Math. 3(1):50–73.Crossref, Google Scholar
• Lai TL, Robbins H (1985) Asymptotically efficient adaptive allocation rules. Adv. Appl. Math. 6(1):4–22.Crossref, Google Scholar
• Lai TL, Wei CZ (1982) Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Ann. Statist. 10(1):154–166.Crossref, Google Scholar
• Lai TL, Robbins H, Wei CZ (1979) Strong consistency of least squares estimates in multiple regression II. J. Multivariate Anal. 9(3):343–361.Crossref, Google Scholar
• Lim AEB, Shanthikumar JG (2007) Relative entropy, exponential utility, and robust dynamic pricing. Oper. Res. 55(2):198–214.Link, Google Scholar
• Lin KY (2006) Dynamic pricing with real-time demand learning. Eur. J. Oper. Res. 174(1):522–538.Crossref, Google Scholar
• Lobo MS, Boyd S (2003) Pricing and learning with uncertain demand. Working paper, Stanford University, Stanford, CA. http://www.stanford.edu/~boyd/papers/pdf/pric_learn_unc_dem.pdf.Google Scholar
• McCullagh P (1983) Quasi-likelihood functions. Ann. Statist. 11(1):59–67.Crossref, Google Scholar
• McCullagh P, Nelder JA (1983) Generalized Linear Models (Chapman & Hall, London).Crossref, Google Scholar
• McLennan A (1984) Price dispersion and incomplete learning in the long run. J. Econom. Dynam. Control 7(3):331–347.Crossref, Google Scholar
• Nassiri-Toussi K, Ren W (1994) On the convergence of least squares estimates in white noise. IEEE Trans. Automatic Control 39(2):364–368.Crossref, Google Scholar
• Powell WB (2010) The knowledge gradient for optimal learning. Cochran JJ, Cox LA Jr, Keskinocak P, Kharoufeh JP, Smith JC, eds. Encyclopedia of Operations Research and Management Science (John Wiley & Sons, New York).Google Scholar
• Robbins H, Monro S (1951) A stochastic approximation method. Ann. Math. Statist. 22(3):400–407.Crossref, Google Scholar
• Taylor JB (1974) Asymptotic properties of multiperiod control rules in the linear regression model. Internat. Econom. Rev. 15(2):472–484.Crossref, Google Scholar
• Vermorel J, Mohri M (2005) Multi-armed bandit algorithms and empirical evaluation. Gama J, Camacho R, Brazdil P, Jorge A, Torgo L, eds. Proceedings of the 16th European Conference on Machine Learning, Lecture Notes in Computer Science, Vol. 3720 (Springer-Verlag, Berlin), 437–448.Crossref, Google Scholar
• Wedderburn RWM (1974) Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61(3):439–447.Google Scholar