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A Parametric Contextual Online Learning Theory of Brokerage

Author

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  • Franc{c}ois Bachoc
  • Tommaso Cesari
  • Roberto Colomboni

Abstract

We study the role of contextual information in the online learning problem of brokerage between traders. In this sequential problem, at each time step, two traders arrive with secret valuations about an asset they wish to trade. The learner (a broker) suggests a trading (or brokerage) price based on contextual data about the asset and the market conditions. Then, the traders reveal their willingness to buy or sell based on whether their valuations are higher or lower than the brokerage price. A trade occurs if one of the two traders decides to buy and the other to sell, i.e., if the broker's proposed price falls between the smallest and the largest of their two valuations. We design algorithms for this problem and prove optimal theoretical regret guarantees under various standard assumptions.

Suggested Citation

  • Franc{c}ois Bachoc & Tommaso Cesari & Roberto Colomboni, 2024. "A Parametric Contextual Online Learning Theory of Brokerage," Papers 2407.01566, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2407.01566
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    References listed on IDEAS

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    1. repec:hal:journl:hal-04475574 is not listed on IDEAS
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    6. Jianqing Fan & Yongyi Guo & Mengxin Yu, 2024. "Policy Optimization Using Semiparametric Models for Dynamic Pricing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 552-564, January.
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