Long-Term Online Smoothing Prediction Using Expert Advice

For the prediction with experts' advice setting, we construct forecasting algorithms that suffer loss not much more than any expert in the pool. In contrast to the standard approach, we investigate the case of long-term forecasting of time series and consider two scenarios. In the first one, at each step $t$ the learner has to combine the point forecasts of the experts issued for the time interval $[t+1, t+d]$ ahead. Our approach implies that at each time step experts issue point forecasts for arbitrary many steps ahead and then the learner (algorithm) combines these forecasts and the forecasts made earlier into one vector forecast for steps $[t+1,t+d]$. By combining past and the current long-term forecasts we obtain a smoothing mechanism that protects our algorithm from temporary trend changes, noise and outliers. In the second scenario, at each step $t$ experts issue a prediction function, and the learner has to combine these functions into the single one, which will be used for long-term time-series prediction. For each scenario, we develop an algorithm for combining experts forecasts and prove $O(\ln T)$ adversarial regret upper bound for both algorithms.