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Constrained no-regret learning

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  • Du, Ye
  • Lehrer, Ehud

Abstract

We investigate a dynamic decision making problem with constraints. The decision maker is free to take any action as long as the empirical frequency of the actions played does not violate pre-specified constraints. In a case of violation the decision maker is penalized. We introduce the constrained no-regret learning model. In this model the set of alternative strategies, with which a dynamic decision policy is compared, is the set of stationary mixed actions that satisfy all the constraints. We show that there exists a strategy that satisfies the following properties: (i) it guarantees that after an unavoidable deterministic grace period, there are absolutely no violations; (ii) for an arbitrarily small constant ϵ>0, it achieves a convergence rate of T−1−ϵ2, which improves the O(T−13) convergence rate of Mannor et al. (2009).

Suggested Citation

  • Du, Ye & Lehrer, Ehud, 2020. "Constrained no-regret learning," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 16-24.
    • Handle: RePEc:eee:mateco:v:88:y:2020:i:c:p:16-24
    DOI: 10.1016/j.jmateco.2020.02.002
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    References listed on IDEAS

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    Cited by:

    1. Fournier, Gaëtan & Kuperwasser, Eden & Munk, Orin & Solan, Eilon & Weinbaum, Avishay, 2021. "Approachability with constraints," European Journal of Operational Research, Elsevier, vol. 292(2), pages 687-695.

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