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Online Allocation and Pricing: Constant Regret via Bellman Inequalities

Author

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  • Alberto Vera

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

  • Siddhartha Banerjee

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

  • Itai Gurvich

    (Kellogg School of Management, Northwestern University, Evanston, Illinois 60208)

Abstract

We develop a framework for designing simple and efficient policies for a family of online allocation and pricing problems that includes online packing, budget-constrained probing, dynamic pricing, and online contextual bandits with knapsacks. In each case, we evaluate the performance of our policies in terms of their regret (i.e., additive gap) relative to an offline controller that is endowed with more information than the online controller. Our framework is based on Bellman inequalities, which decompose the loss of an algorithm into two distinct sources of error: (1) arising from computational tractability issues, and (2) arising from estimation/prediction of random trajectories. Balancing these errors guides the choice of benchmarks, and leads to policies that are both tractable and have strong performance guarantees. In particular, in all our examples, we demonstrate constant-regret policies that only require resolving a linear program in each period, followed by a simple greedy action-selection rule; thus, our policies are practical as well as provably near optimal.

Suggested Citation

  • Alberto Vera & Siddhartha Banerjee & Itai Gurvich, 2021. "Online Allocation and Pricing: Constant Regret via Bellman Inequalities," Operations Research, INFORMS, vol. 69(3), pages 821-840, May.
  • Handle: RePEc:inm:oropre:v:69:y:2021:i:3:p:821-840
    DOI: 10.1287/opre.2020.2061
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    References listed on IDEAS

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    1. 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.
    2. Santiago R. Balseiro & David B. Brown, 2019. "Approximations to Stochastic Dynamic Programs via Information Relaxation Duality," Operations Research, INFORMS, vol. 67(2), pages 577-597, March.
    3. Niv Buchbinder & Kamal Jain & Mohit Singh, 2014. "Secretary Problems via Linear Programming," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 190-206, February.
    4. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-654, May.
    5. Qi (George) Chen & Stefanus Jasin & Izak Duenyas, 2019. "Nonparametric Self-Adjusting Control for Joint Learning and Optimization of Multiproduct Pricing with Finite Resource Capacity," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 601-631, May.
    6. Stefanus Jasin, 2014. "Reoptimization and Self-Adjusting Price Control for Network Revenue Management," Operations Research, INFORMS, vol. 62(5), pages 1168-1178, October.
    7. David B. Brown & James E. Smith & Peng Sun, 2010. "Information Relaxations and Duality in Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 785-801, August.
    8. Stefanus Jasin & Sunil Kumar, 2012. "A Re-Solving Heuristic with Bounded Revenue Loss for Network Revenue Management with Customer Choice," Mathematics of Operations Research, INFORMS, vol. 37(2), pages 313-345, May.
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    Cited by:

    1. Süleyman Kerimov & Itai Ashlagi & Itai Gurvich, 2024. "Dynamic Matching: Characterizing and Achieving Constant Regret," Management Science, INFORMS, vol. 70(5), pages 2799-2822, May.

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