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A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint

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  • Ningyuan Chen
  • Guillermo Gallego

Abstract

We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed but the demand function associated with each type is initially unknown. The firm sets personalized prices dynamically for each type and attempts to maximize the revenue over the season. We provide a learning algorithm that is near-optimal when the demand and capacity scale in proportion. The algorithm utilizes the primal-dual formulation of the problem and learns the dual optimal solution explicitly. It allows the algorithm to overcome the curse of dimensionality (the rate of regret is independent of the number of types) and sheds light on novel algorithmic designs for learning problems with resource constraints.

Suggested Citation

  • Ningyuan Chen & Guillermo Gallego, 2018. "A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint," Papers 1812.09234, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:1812.09234
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    References listed on IDEAS

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    1. Omar Besbes & Assaf Zeevi, 2012. "Blind Network Revenue Management," Operations Research, INFORMS, vol. 60(6), pages 1537-1550, December.
    2. Victor F. Araman & René Caldentey, 2009. "Dynamic Pricing for Nonperishable Products with Demand Learning," Operations Research, INFORMS, vol. 57(5), pages 1169-1188, October.
    3. Vivek F. Farias & Benjamin Van Roy, 2010. "Dynamic Pricing with a Prior on Market Response," Operations Research, INFORMS, vol. 58(1), pages 16-29, February.
    4. Guillermo Gallego & Garrett van Ryzin, 1997. "A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management," Operations Research, INFORMS, vol. 45(1), pages 24-41, February.
    5. N. Bora Keskin & Assaf Zeevi, 2014. "Dynamic Pricing with an Unknown Demand Model: Asymptotically Optimal Semi-Myopic Policies," Operations Research, INFORMS, vol. 62(5), pages 1142-1167, October.
    6. Sébastien Bubeck & Rémi Munos & Gilles Stoltz & Csaba Szepesvari, 2011. "X-Armed Bandits," Post-Print hal-00450235, HAL.
    7. Arnoud V. den Boer & Bert Zwart, 2014. "Simultaneously Learning and Optimizing Using Controlled Variance Pricing," Management Science, INFORMS, vol. 60(3), pages 770-783, March.
    8. Josef Broder & Paat Rusmevichientong, 2012. "Dynamic Pricing Under a General Parametric Choice Model," Operations Research, INFORMS, vol. 60(4), pages 965-980, August.
    9. Omar Besbes & Assaf Zeevi, 2009. "Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms," Operations Research, INFORMS, vol. 57(6), pages 1407-1420, December.
    10. Arnoud V. den Boer & Bert Zwart, 2015. "Dynamic Pricing and Learning with Finite Inventories," Operations Research, INFORMS, vol. 63(4), pages 965-978, August.
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