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Active Learning for Contextual Search with Binary Feedback

Author

Listed:
  • Xi Chen

    (Leonard N. Stern School of Business, New York University, New York, New York 10012)

  • Quanquan Liu

    (Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080)

  • Yining Wang

    (Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080)

Abstract

In this paper, we study the learning problem in contextual search, which is motivated by applications such as crowdsourcing and personalized medicine experiments. In particular, for a sequence of arriving context vectors, with each context associated with an underlying value, the decision maker either makes a query at a certain point or skips the context. The decision maker will only observe the binary feedback on the relationship between the query point and the value associated with the context. We study a probably approximately correct learning setting, where the goal is to learn the underlying mean value function in context with a minimum number of queries. To address this challenge, we propose a trisection search approach combined with a margin-based active learning method. We show that the algorithm only needs to make O ˜ ( 1 / ε 2 ) queries to achieve an ε -estimation accuracy. This sample complexity significantly reduces the required sample complexity in the passive setting where neither sample skipping nor query selection is allowed, which is at least Ω ( 1 / ε 3 ) .

Suggested Citation

  • Xi Chen & Quanquan Liu & Yining Wang, 2023. "Active Learning for Contextual Search with Binary Feedback," Management Science, INFORMS, vol. 69(4), pages 2165-2181, April.
    • Handle: RePEc:inm:ormnsc:v:69:y:2023:i:4:p:2165-2181
    DOI: 10.1287/mnsc.2022.4473
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    References listed on IDEAS

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    1. Maxime C. Cohen & Ilan Lobel & Renato Paes Leme, 2020. "Feature-Based Dynamic Pricing," Management Science, INFORMS, vol. 66(11), pages 4921-4943, November.
    2. Hamsa Bastani & Mohsen Bayati, 2020. "Online Decision Making with High-Dimensional Covariates," Operations Research, INFORMS, vol. 68(1), pages 276-294, January.
    3. Li, Xiaoou & Chen, Yunxiao & Chen, Xi & Liu, Jingchen & Ying, Zhiliang, 2021. "Optimal stopping and worker selection in crowdsourcing: an adaptive sequential probability ratio test framework," LSE Research Online Documents on Economics 100873, London School of Economics and Political Science, LSE Library.
    4. Hamsa Bastani & Mohsen Bayati & Khashayar Khosravi, 2021. "Mostly Exploration-Free Algorithms for Contextual Bandits," Management Science, INFORMS, vol. 67(3), pages 1329-1349, March.
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    Cited by:

    1. Jinglong Zhao, 2024. "Experimental Design For Causal Inference Through An Optimization Lens," Papers 2408.09607, arXiv.org, revised Aug 2024.

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