Prediction with expert advice for the Brier game

TL;DR

This paper demonstrates the mixability of the Brier game, derives optimal parameters, and applies the resulting prediction algorithm to sports outcomes, showing tight theoretical guarantees especially for tennis data.

Contribution

It establishes the mixability of the Brier game, finds optimal learning parameters, and applies the method to real sports data with strong performance guarantees.

Findings

The Brier game is proven to be mixable.

Optimal learning rate and substitution function are derived.

Prediction algorithm performs well on football and tennis data.

Abstract

We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical performance guarantee turns out to be rather tight on these data sets, especially in the case of the more extensive tennis data.