A PDE approach for regret bounds under partial monitoring
Erhan Bayraktar, Ibrahim Ekren, Xin Zhang; 24(299):1−24, 2023.
In this paper, we study a learning problem in which a forecaster only observes partial information. By properly rescaling the problem, we heuristically derive a limiting PDE on Wasserstein space which characterizes the asymptotic behavior of the regret of the forecaster. Using a verification type argument, we show that the problem of obtaining regret bounds and efficient algorithms can be tackled by finding appropriate smooth sub/supersolutions of this parabolic PDE.
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