Adaptive Algorithm of Tracking the Best Experts Trajectory

Abstract

The problem of decision theoretic online learning is discussed. There is the set of methods, experts, and algorithms capable of making solutions (or predictions) and suffering losses due to the inaccuracy of their solutions. An adaptive algorithm whereby expert solutions are aggregated and sustained losses not exceeding (to a certain quantity called a regret) those of the best combination of experts distributed over the prediction interval is proposed. The algorithm is constructed using the Fixed-Share method combined with the Ada-Hedge algorithm used to exponentially weight expert solutions. The regret of the proposed algorithm is estimated. In the context of the given approach, there are no any stochastic assumptions about an initial data source and the boundedness of losses. The results of numerical experiments concerning the mixing of expert solutions with the help of the proposed algorithm are presented. The strategies of games on financial markets, which were suggested in our previous papers, play the role of expert strategies.