Prediction against a limited adversary

Erhan Bayraktar, Ibrahim Ekren, Xin Zhang.

Year: 2021, Volume: 22, Issue: 72, Pages: 1−33


We study the problem of prediction with expert advice with adversarial corruption where the adversary can at most corrupt one expert. Using tools from viscosity theory, we characterize the long-time behavior of the value function of the game between the forecaster and the adversary. We provide lower and upper bounds for the growth rate of regret without relying on a comparison result. We show that depending on the description of regret, the limiting behavior of the game can significantly differ.