Tracking the Optimal Sequence of Predictive Strategies

Abstract

Within the prediction (decision making) theory with online experts, an adaptive algorithm is proposed that aggregates the decisions of expert strategies and incurs losses that do not exceed (up to a certain value, called a regret) the losses of the best combination of experts distributed over the prediction interval. The algorithm develops the Mixing Past Posteriors method and the AdaHedge algorithm of exponential weighting of expert decisions using an adaptive learning parameter. An estimate of the regret of the proposed algorithm is obtained. The approach proposed does not make assumptions about the nature of the data source and the limits of experts’ losses. The results of numerical experiments on mixing expert solutions using the proposed algorithm under conditions of high volatility of experts’ losses are given.