Calibration with many checking rules
Mathematics of Operations Research
Prediction, Learning, and Games
Prediction, Learning, and Games
Deterministic calibration and Nash equilibrium
Journal of Computer and System Sciences
Online Learning with Sample Path Constraints
The Journal of Machine Learning Research
Convex primal decomposition for multicarrier linear MIMO transceivers
IEEE Transactions on Signal Processing
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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.