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We consider a sequence of repeated prediction games and formally pass to the limit. The supersolutions of the resulting non-linear parabolic partial differential equation are closely related to the potential functions in the sense of N.,Cesa-Bianci, G.,Lugosi (2003). Any such supersolution gives an upper bound for forecasteru0027s regret and suggests a potential-based prediction strategy, satisfying the Blackwell condition. A conventional upper bound for the worst-case regret is justified by a simple verification argument.

PDE APPROACH TO THE PROBLEM OF ONLINE PREDICTION WITH EXPERT ADVICE: A CONSTRUCTION OF POTENTIAL-BASED STRATEGIES