A Geometric Proof of Calibration

G. STOLTZ, S. Mannor

Mathematics of Operations Research

novembre 2010, vol. 35, n°4, pp.721-727

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Mots clés : Calibration, Approachability, Convergence rates, Computational complexity

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