A Geometric Proof of Calibration

Gilles Stoltz and Shie Mannor ()
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Shie Mannor: EE-Technion - Department of Electrical Engineering - Technion [Haïfa] - Technion - Israel Institute of Technology [Haifa]

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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.

Keywords: calibration; approachability; convergence rates; computational complexity (search for similar items in EconPapers)
Date: 2010-11
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Citations: View citations in EconPapers (4)

Published in Mathematics of Operations Research, 2010, 35 (4), pp.721-727. ⟨10.1287/moor.1100.0465⟩

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Working Paper: A Geometric Proof of Calibration (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00586044

DOI: 10.1287/moor.1100.0465

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