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A Geometric Proof of Calibration

Author

Listed:
  • Gilles Stoltz

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Shie Mannor

    (EE-Technion - Department of Electrical Engineering - Technion [Haïfa] - Technion - Israel Institute of Technology [Haifa])

Abstract

We provide yet another proof of the existence of calibrated forecasters; it has two merits. First, it is valid for an arbitrary finite number of outcomes. Second, it is short and simple and it follows from a direct application of Blackwell's approachability theorem to a carefully chosen vector-valued payoff function and convex target set. Our proof captures the essence of existing proofs based on approachability (e.g., the proof by Foster [Foster, D. 1999. A proof of calibration via Blackwell's approachability theorem. Games Econom. Behav. 29 73-78] in the case of binary outcomes) and highlights the intrinsic connection between approachability and calibration.

Suggested Citation

  • Gilles Stoltz & Shie Mannor, 2010. "A Geometric Proof of Calibration," Post-Print hal-00586044, HAL.
    • Handle: RePEc:hal:journl:hal-00586044
    DOI: 10.1287/moor.1100.0465
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    Cited by:

    1. Dean Foster & Rakesh Vohra, 2011. "Calibration: Respice, Adspice, Prospice," Discussion Papers 1537, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Olszewski, Wojciech, 2015. "Calibration and Expert Testing," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Vladimir V'yugin, 2014. "Log-Optimal Portfolio Selection Using the Blackwell Approachability Theorem," Papers 1410.5996, arXiv.org, revised Jun 2015.
    4. Vianney Perchet, 2015. "Exponential Weight Approachability, Applications to Calibration and Regret Minimization," Dynamic Games and Applications, Springer, vol. 5(1), pages 136-153, March.
    5. Andrey Bernstein & Shie Mannor & Nahum Shimkin, 2014. "Opportunistic Approachability and Generalized No-Regret Problems," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1057-1083, November.

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