Greedy Model Averaging

This paper considers the problem of combining multiple models to achieve a prediction accuracy not much worse than that of the best single model for least squares regression. It is known that if the models are mis-specified, model averaging is superior to model selection. Specifically, let $n$ be the sample size, then the worst case regret of the former decays at the rate of $O(1/n)$ while the worst case regret of the latter decays at the rate of $O(1/\sqrt{n})$. In the literature, the most important and widely studied model averaging method that achieves the optimal $O(1/n)$ average regret is the exponential weighted model averaging (EWMA) algorithm. However this method suffers from several limitations. The purpose of this paper is to present a new greedy model averaging procedure that improves EWMA. We prove strong theoretical guarantees for the new procedure and illustrate our theoretical results with empirical examples.