A PDE approach for regret bounds under partial monitoring

Erhan Bayraktar, Ibrahim Ekren, Xin Zhang.

Year: 2023, Volume: 24, Issue: 299, Pages: 1−24


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.