Foster, Dean PRakhlin, AlexanderSridharan, KarthikTewari, Ambuj2023-05-232023-05-232011-01-012016-08-19https://repository.upenn.edu/handle/20.500.14332/47495We consider the problem of forecasting a sequence of outcomes from an unknown source. The quality of the forecaster is measured by a family of checking rules. We prove upper bounds on the value of the associated game, thus certifying the existence of a calibrated strategy for the forecaster. We show that complexity of the family of checking rules can be captured by the notion of a sequential cover introduced in [19]. Various natural assumptions on the class of checking rules are considered, including finiteness of Vapnik-Chervonenkis and Littlestone's dimensions.Statistics and ProbabilityPresentation