Online aggregation of unbounded losses using shifting experts with confidence

摘要

We develop the setting of sequential prediction based on shifting experts and on a “smooth” version of the method of specialized experts. To aggregate expert predictions, we use the AdaHedge algorithm, which is a version of the Hedge algorithm with adaptive learning rate, and extend it by the meta-algorithm Fixed Share. Due to this, we combine the advantages of both algorithms: (1) we use the shifting regret which is a more optimal characteristic of the algorithm; (2) regret bounds are valid in the case of signed unbounded losses of the experts. Also, (3) we incorporate in this scheme a “smooth” version of the method of specialized experts which allows us to make more flexible and accurate predictions. All results are obtained in the adversarial setting—no assumptions are made about the nature of the data source. We present results of numerical experiments for short-term forecasting of electricity consumption based on real data.