Offline Feature-Based Pricing Under Censored Demand: A Causal Inference Approach

References

• Aalen O (1978) Nonparametric inference for a family of counting processes. Ann. Statist. 6(4):701–726.Crossref, Google Scholar
• Agrawal S, Jia R (2022) Learning in structured MDPs with convex cost functions: Improved regret bounds for inventory management. Oper. Res. 70(3):1646–1664.Link, Google Scholar
• Agrawal N, Smith SA (1996) Estimating negative binomial demand for retail inventory management with unobservable lost sales. Naval Res. Logist. 43(6):839–861.Crossref, Google Scholar
• Ban GY, Keskin NB (2021) Personalized dynamic pricing with machine learning: High-dimensional features and heterogeneous elasticity. Management Sci. 67(9):5549–5568.Link, Google Scholar
• Bang H, Robins JM (2005) Doubly robust estimation in missing data and causal inference models. Biometrics 61(4):962–973.Crossref, Google Scholar
• Barron AR (1994) Approximation and estimation bounds for artificial neural networks. Machine Learn. 14(1):115–133.Crossref, Google Scholar
• Bensoussan A, Sethi SP (2009) A note on “the censored newsvendor and the optimal acquisition of information.” Oper. Res. 57(3):791–794.Link, Google Scholar
• Bensoussan A, Cakanyildirim M, Sethi S (2009) Censored newsvendor model revisited with unnormalized probabilities. J. Indust. Management Optim. 5(2):391–402.Crossref, Google Scholar
• Besbes O, Muharremoglu A (2013) On implications of demand censoring in the newsvendor problem. Management Sci. 59(6):1407–1424.Link, Google Scholar
• Bickel PJ (1982) On adaptive estimation. Ann. Statist. 10(3):647–671.Crossref, Google Scholar
• Biggs M (2022) Convex surrogate loss functions for contextual pricing with transaction data. Preprint, submitted February 16, https://arxiv.org/abs/2202.10944.Google Scholar
• Biggs M, Gao R, Sun W (2021) Loss functions for discrete contextual pricing with observational data. Preprint, submitted November 18, https://arxiv.org/abs/2111.09933.Google Scholar
• Bisi A, Dada M (2007) Dynamic learning, pricing, and ordering by a censored newsvendor. Naval Res. Logist. 54(4):448–461.Crossref, Google Scholar
• Bisi A, Dada M, Tokdar S (2011) A censored-data multiperiod inventory problem with newsvendor demand distributions. Manufacturing Service Oper. Management 13(4):525–533.Link, Google Scholar
• Bu J, Simchi-Levi D, Wang L (2023) Offline pricing and demand learning with censored data. Management Sci. 69(2):885–903.Link, Google Scholar
• Bu J, Simchi-Levi D, Xu Y (2022) Online pricing with offline data: Phase transition and inverse square law. Management Sci. 68(12):8568–8588.Link, Google Scholar
• Cai H, Shi C, Song R, Lu W (2021) Jump interval-learning for individualized decision making. Preprint, submitted November 17, https://arxiv.org/abs/2111.08885.Google Scholar
• Chen B, Chao X (2020) Dynamic inventory control with stockout substitution and demand learning. Management Sci. 66(11):5108–5127.Link, Google Scholar
• Chen B, Chao X, Ahn HS (2019) Coordinating pricing and inventory replenishment with nonparametric demand learning. Oper. Res. 67(4):1035–1052.Abstract, Google Scholar
• Chen B, Chao X, Shi C (2021a) Nonparametric learning algorithms for joint pricing and inventory control with lost sales and censored demand. Math. Oper. Res. 46(2):726–756.Link, Google Scholar
• Chen B, Chao X, Wang Y (2020) Data-based dynamic pricing and inventory control with censored demand and limited price changes. Oper. Res. 68(5):1445–1456.Link, Google Scholar
• Chen B, Simchi-Levi D, Wang Y, Zhou Y (2022a) Dynamic pricing and inventory control with fixed ordering cost and incomplete demand information. Management Sci. 68(8):5684–5703.Link, Google Scholar
• Chen G, Zeng D, Kosorok MR (2016) Personalized dose finding using outcome weighted learning. J. Amer. Statist. Assoc. 111(516):1509–1521.Crossref, Google Scholar
• Chen N, Gallego G (2021) Nonparametric pricing analytics with customer covariates. Oper. Res. 69(3):974–984.Link, Google Scholar
• Chen X (2007) Large sample sieve estimation of semi-nonparametric models. Handbook Econometrics 6(76):5549–5632.Crossref, Google Scholar
• Chen X, Simchi-Levi D (2006) Coordinating inventory control and pricing strategies: The continuous review model. Oper. Res. Lett. 34(3):323–332.Crossref, Google Scholar
• Chen X, Miao S, Wang Y (2023a) Differential privacy in personalized pricing with nonparametric demand models. Oper. Res. 71(2):581–602.Link, Google Scholar
• Chen X, Simchi-Levi D, Wang Y (2022b) Privacy-preserving dynamic personalized pricing with demand learning. Management Sci. 68(7):4878–4898.Link, Google Scholar
• Chen X, Simchi-Levi D, Wang Y (2023b) Utility fairness in contextual dynamic pricing with demand learning. Preprint, submitted November 28, https://arxiv.org/abs/2311.16528.Google Scholar
• Chen X, Zhang X, Zhou Y (2021b) Fairness-aware online price discrimination with nonparametric demand models. Preprint, submitted November 16, https://arxiv.org/abs/2111.08221.Google Scholar
• Chernozhukov V, Chetverikov D, Kato K (2014) Gaussian approximation of suprema of empirical processes. Ann. Statist. 42(4):1564–1597.Crossref, Google Scholar
• Chernozhukov V, Demirer M, Lewis G, Syrgkanis V (2019) Semi-parametric efficient policy learning with continuous actions. Wallach H, Larochelle H, Beygelzimer A, d’Alché-Buc F, Fox E, Garnett R, eds. Adv. Neural Inform. Processing Systems, vol. 32 (Curran Associates, Inc., New York), 1–9.Google Scholar
• Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C, Newey W, Robins J (2018) Double/debiased machine learning for treatment and structural parameters. Econom. J. 21(1):1–68.Crossref, Google Scholar
• Cheung WC, Simchi-Levi D (2019) Sampling-based approximation schemes for capacitated stochastic inventory control models. Math. Oper. Res. 44(2):668–692.Link, Google Scholar
• Cohen MC, Elmachtoub AN, Lei X (2022) Price discrimination with fairness constraints. Management Sci. 68(12):8536–8552.Link, Google Scholar
• Cohen MC, Lobel I, Paes Leme R (2020) Feature-based dynamic pricing. Management Sci. 66(11):4921–4943.Link, Google Scholar
• Cohen MC, Miao S, Wang Y (2021) Dynamic pricing with fairness constraints. Preprint, submitted September 28, https://dx.doi.org/10.2139/ssrn.3930622.Google Scholar
• Columbus L (2020) 10 ways AI improves pricing and revenue management. Forbes Online (September 7), https://www.forbes.com/sites/louiscolumbus/2020/09/07/10-ways-ai-improves-pricing-and-revenue-management/?sh=6b05cf972f33.Google Scholar
• Conrad S (1976) Sales data and the estimation of demand. J. Oper. Res. Soc. 27(1):123–127.Crossref, Google Scholar
• Cui Y, Pang JS, Sen B (2018) Composite difference-max programs for modern statistical estimation problems. SIAM J. Optim. 28(4):3344–3374.Crossref, Google Scholar
• Cui Y, Zhu R, Kosorok M (2017) Tree based weighted learning for estimating individualized treatment rules with censored data. Electronic J. Statist. 11(2):3927–3953.Crossref, Google Scholar
• Dabrowska DM (1989) Uniform consistency of the kernel conditional Kaplan–Meier estimate. Ann. Statist. 17(3):1157–1167.Crossref, Google Scholar
• Den Boer AV (2015) Dynamic pricing and learning: Historical origins, current research, and new directions. Surveys Oper. Res. Management Sci. 20(1):1–18.Crossref, Google Scholar
• Diggle P, Kenward MG (1994) Informative drop-out in longitudinal data analysis. J. Roy. Statist. Soc. Ser. C Appl. Statist. 43(1):49–73.Google Scholar
• Elmachtoub A, Gupta V, Hamilton ML (2021) The value of personalized pricing. Management Sci. 67(10):6055–6070.Link, Google Scholar
• Elmachtoub A, Gupta V, Zhao Y (2023) Balanced off-policy evaluation for personalized pricing. Ruiz F, Dy J, van de Meent JW, eds. Proc. 26th Internat. Conf. Artificial Intelligence Statist., vol. 206 (PMLR, New York), 10901–10917.Google Scholar
• Fan J, Guo Y, Yu M (2024) Policy optimization using semiparametric models for dynamic pricing. J. Amer. Statist. Assoc. 119(545):552–564.Crossref, Google Scholar
• Feng Q, Shanthikumar JG (2018) How research in production and operations management may evolve in the era of big data. Production Oper. Management 27(9):1670–1684.Crossref, Google Scholar
• Ferreira KJ, Lee BHA, Simchi-Levi D (2016) Analytics for an online retailer: Demand forecasting and price optimization. Manufacturing Service Oper. Management 18(1):69–88.Link, Google Scholar
• Foster DJ, Krishnamurthy A, Simchi-Levi D, Xu Y (2021) Offline reinforcement learning: Fundamental barriers for value function approximation. Preprint, submitted November 21, https://arxiv.org/abs/2111.10919.Google Scholar
• Garcia D, Tolvanen J, Wagner AK (2022) Demand estimation using managerial responses to automated price recommendations. Management Sci. 68(11):7918–7939.Link, Google Scholar
• Geurts P, Ernst D, Wehenkel L (2006) Extremely randomized trees. Machine Learn. 63(1):3–42.Crossref, Google Scholar
• Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y (2014) Generative adversarial nets. Ghahramani Z, Welling M, Cortes C, Lawrence N, Weinberger K, eds. Adv. Neural Inform. Processing Systems, vol. 27 (Curran Associates, Inc., New York), 1–9.Google Scholar
• Hirano K, Imbens GW (2004) The propensity score with continuous treatments. Appl. Bayesian Model. Causal Inference Incomplete-Data Perspect. 1(7):73–84.Google Scholar
• Huh WT, Rusmevichientong P (2009) A nonparametric asymptotic analysis of inventory planning with censored demand. Math. Oper. Res. 34(1):103–123.Link, Google Scholar
• Huh WT, Janakiraman G, Muckstadt JA, Rusmevichientong P (2009) An adaptive algorithm for finding the optimal base-stock policy in lost sales inventory systems with censored demand. Math. Oper. Res. 34(2):397–416.Link, Google Scholar
• Huh WT, Levi R, Rusmevichientong P, Orlin JB (2011) Adaptive data-driven inventory control with censored demand based on Kaplan–Meier estimator. Oper. Res. 59(4):929–941.Link, Google Scholar
• Imbens GW, Rubin DB (2015) Causal Inference in Statistics, Social, and Biomedical Sciences (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• Ishwaran H, Kogalur UB, Blackstone EH, Lauer MS (2008) Random survival forests. Ann. Appl. Statist. 2(3):841–860.Crossref, Google Scholar
• Javanmard A, Nazerzadeh H (2019) Dynamic pricing in high-dimensions. J. Machine Learn. Res. 20(1):315–363.Google Scholar
• Jin Y, Yang Z, Wang Z (2021) Is pessimism provably efficient for offline RL? Meila M, Zhang T, eds. Proc. 38th Internat. Conf. Machine Learn., vol. 139 (PMLR, New York), 5084–5096.Google Scholar
• Kallus N, Zhou A (2018) Policy evaluation and optimization with continuous treatments. Storkey A, Perez-Cruz F, eds. Proc. 38th Internat. Conf. Machine Learn., vol. 84 (PMLR, New York), 1243–1251.Google Scholar
• Khardani S, Semmar S (2014) Nonparametric conditional density estimation for censored data based on a recursive kernel. Electronic J. Statist. 8(2):2541–2556.Crossref, Google Scholar
• Kingma DP, Ba J (2017) Adam: A method for stochastic optimization. Bengio Y, LeCun Y, eds. Internat. Conf. Learn. Representations, vol. 13 (PMLR, New York), 1–9.Google Scholar
• Kleinbaum DG, Klein M (2010) Survival Analysis (Springer, New York).Google Scholar
• Kosorok MR, Laber EB (2019) Precision medicine. Annual Rev. Statist. Appl. 6(1):263–286.Crossref, Google Scholar
• Lee D, Hosanagar K (2021) How do product attributes and reviews moderate the impact of recommender systems through purchase stages? Management Sci. 67(1):524–546.Link, Google Scholar
• Levi R, Perakis G, Uichanco J (2015) The data-driven newsvendor problem: New bounds and insights. Oper. Res. 63(6):1294–1306.Link, Google Scholar
• Levi R, Roundy RO, Shmoys DB (2007) Provably near-optimal sampling-based policies for stochastic inventory control models. Math. Oper. Res. 32(4):821–839.Link, Google Scholar
• Liu J, Qin H, Chou MC (2023a) Pricing analytics with shape-restricted demands. Preprint, submitted December 1, https://dx.doi.org/10.2139/ssrn.4643942.Google Scholar
• Liu P, Yang Z, Wang Z, Sun WW (2023b) Contextual dynamic pricing with strategic buyers. Preprint, submitted July 8, https://arxiv.org/abs/2307.04055.Google Scholar
• Lu X, Song JS, Zhu K (2005) On “the censored newsvendor and the optimal acquisition of information.” Oper. Res. 53(6):1024–1026.Link, Google Scholar
• Lugosi G, Markakis MG, Neu G (2017) On the hardness of inventory management with censored demand data. Preprint, submitted October 16, https://arxiv.org/abs/1710.05739.Google Scholar
• Luo Y, Sun WW, Liu Y (2024) Distribution-free contextual dynamic pricing. Math. Oper. Res. 49(1):599–618.Link, Google Scholar
• Mersereau AJ (2015) Demand estimation from censored observations with inventory record inaccuracy. Manufacturing Service Oper. Management 17(3):335–349.Link, Google Scholar
• Miao R, Qi Z, Shi C, Lin L (2023) Personalized pricing with invalid instrumental variables: Identification, estimation, and policy learning. Technical report, George Washington University, Washington, DC.Google Scholar
• Miao S, Chen X, Chao X, Liu J, Zhang Y (2022) Context-based dynamic pricing with online clustering. Production Oper. Management 31(9):3559–3575.Crossref, Google Scholar
• Micchelli CA, Xu Y, Zhang H (2006) Universal kernels. J. Machine Learn. Res. 7(12):2651–2667.Google Scholar
• Nahmias S (1994) Demand estimation in lost sales inventory systems. Naval Res. Logist. 41(6):739–757.Crossref, Google Scholar
• Nambiar M, Simchi-Levi D, Wang H (2019) Dynamic learning and pricing with model misspecification. Management Sci. 65(11):4980–5000.Link, Google Scholar
• Nelson W (1972) Theory and applications of hazard plotting for censored failure data. Technometrics 14(4):945–966.Crossref, Google Scholar
• Parzen E (1962) On estimation of a probability density function and mode. Ann. Math. Statist. 33(3):1065–1076.Crossref, Google Scholar
• Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, et al. (2011) Scikit-learn: Machine learning in Python. J. Machine Learn. Res. 12(1):2825–2830.Google Scholar
• Qiang S, Bayati M (2016) Dynamic pricing with demand covariates. Preprint, submitted April 25, https://dx.doi.org/10.2139/ssrn.2765257.Google Scholar
• Qin H, Simchi-Levi D, Wang L (2022) Data-driven approximation schemes for joint pricing and inventory control models. Management Sci. 68(9):6591–6609.Link, Google Scholar
• Robins J (1986) A new approach to causal inference in mortality studies with a sustained exposure period—Application to control of the healthy worker survivor effect. Math. Model. 7(9–12):1393–1512.Crossref, Google Scholar
• Rosenbaum PR, Rubin DB (1983) The central role of the propensity score in observational studies for causal effects. Biometrika 70(1):41–55.Crossref, Google Scholar
• Rubin DB (1974) Estimating causal effects of treatments in randomized and nonrandomized studies. J. Ed. Psych. 66(5):688–701.Crossref, Google Scholar
• Schmidt-Hieber J (2020) Nonparametric regression using deep neural networks with ReLU activation function. Ann. Statist. 48(4):1875–1897.Google Scholar
• Schulz J, Moodie EE (2021) Doubly robust estimation of optimal dosing strategies. J. Amer. Statist. Assoc. 116(533):256–268.Crossref, Google Scholar
• Simchi-Levi D, Xu Y (2022) Bypassing the monster: A faster and simpler optimal algorithm for contextual bandits under realizability. Math. Oper. Res. 47(3):1904–1931.Link, Google Scholar
• Steinwart I, Christmann A (2008) Support Vector Machines (Springer, New York).Crossref, Google Scholar
• Wang Y, Liu Q (2023) Estimation of high-dimensional contextual pricing models with nonparametric price confounders. Preprint, submitted June 18, https://dx.doi.org/10.2139/ssrn.4482748.Google Scholar
• Wang L, Tchetgen ET (2018) Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables. J. Roy. Statist. Soc. Ser. B Statist. Methodology 80(3):531–550.Crossref, Google Scholar
• Wang T, Brovman YM, Madhvanath S (2021b) Personalized embedding-based e-commerce recommendations at eBay. Preprint, submitted February 11, https://arxiv.org/abs/2102.06156.Google Scholar
• Wang H, Talluri K, Li X (2021a) On dynamic pricing with covariates. Preprint, submitted December 25, https://arxiv.org/abs/2112.13254.Google Scholar
• Wang CH, Wang Z, Sun WW, Cheng G (2020) Online regularization for high-dimensional dynamic pricing algorithms. Preprint, submitted July 5, https://arxiv.org/abs/2007.02470.Google Scholar
• Wecker WE (1978) Predicting demand from sales data in the presence of stockouts. Management Sci. 24(10):1043–1054.Link, Google Scholar
• Xu J, Wang YX (2021) Logarithmic regret in feature-based dynamic pricing. Ranzato M, Beygelzimer A, Dauphin Y, Liang P, Vaughan JW, eds. Adv. Neural Inform. Processing Systems, vol. 34 (Curran Associates, Inc., New York), 13898–13910.Google Scholar
• Ye Z, Zhang Z, Zhang D, Zhang H, Zhang RP (2023) Deep-learning-based causal inference for large-scale combinatorial experiments: Theory and empirical evidence. Preprint, submitted March 14, https://dx.doi.org/10.2139/ssrn.4375327.Google Scholar
• Yuan H, Luo Q, Shi C (2021) Marrying stochastic gradient descent with bandits: Learning algorithms for inventory systems with fixed costs. Management Sci. 67(10):6089–6115.Link, Google Scholar
• Zhang H, Chao X, Shi C (2018) Perishable inventory systems: Convexity results for base-stock policies and learning algorithms under censored demand. Oper. Res. 66(5):1276–1286.Link, Google Scholar
• Zhang H, Chao X, Shi C (2020) Closing the gap: A learning algorithm for lost-sales inventory systems with lead times. Management Sci. 66(5):1962–1980.Link, Google Scholar