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Contextual Search in the Presence of Adversarial Corruptions

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  • Akshay Krishnamurthy
  • Thodoris Lykouris
  • Chara Podimata
  • Robert Schapire

Abstract

We study contextual search, a generalization of binary search in higher dimensions, which captures settings such as feature-based dynamic pricing. Standard formulations of this problem assume that agents act in accordance with a specific homogeneous response model. In practice, however, some responses may be adversarially corrupted. Existing algorithms heavily depend on the assumed response model being (approximately) accurate for all agents and have poor performance in the presence of even a few such arbitrary misspecifications. We initiate the study of contextual search when some of the agents can behave in ways inconsistent with the underlying response model. In particular, we provide two algorithms, one based on multidimensional binary search methods and one based on gradient descent. We show that these algorithms attain near-optimal regret in the absence of adversarial corruptions and their performance degrades gracefully with the number of such agents, providing the first results for contextual search in any adversarial noise model. Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis.

Suggested Citation

  • Akshay Krishnamurthy & Thodoris Lykouris & Chara Podimata & Robert Schapire, 2020. "Contextual Search in the Presence of Adversarial Corruptions," Papers 2002.11650, arXiv.org, revised Aug 2022.
  • Handle: RePEc:arx:papers:2002.11650
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    File URL: http://arxiv.org/pdf/2002.11650
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    References listed on IDEAS

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    1. Virag Shah & Jose Blanchet & Ramesh Johari, 2019. "Semi-parametric dynamic contextual pricing," Papers 1901.02045, arXiv.org, revised Aug 2019.
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    Cited by:

    1. Jianyu Xu & Yu-Xiang Wang, 2022. "Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise," Papers 2201.11341, arXiv.org, revised Apr 2022.

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