Reviews: Online Prediction with Selfish Experts

In this paper, the standard (binary outcome) "prediction with expert advice" setting is altered by treating the experts themselves as players in the game. Specifically, restricting to the class of weight-update algorithms, the experts seek to maximize the weight assigned to them by the algorithm, as a notion of "rating" for their predictions. It is shown that learning algorithms are IC, meaning that experts reveal their true beliefs to the algorithm, if and only if the weight-update function is a strictly proper scoring rule. Because the weighted-majority algorithm (WM) has a weight update which is basically the negative of the loss function, WN is thus IC if and only if the (negative) loss is strictly proper. As the (negative) absolute loss function is not strictly proper, WM is not IC for absolute loss.