Section: Scientific Foundations
Online aggregation of predictors for the prediction of time series, with or without stationarity assumptions
Here, we are concerned with sequential prediction of outcomes, given some base predictions formed by experts. We distinguish two settings, depending on how the sequence of outcomes is generated: it is either

the realization of some stationary process,

or is not modeled at all as the realization of any underlying stochastic process (these sequences are called individual sequences).
The aim is to predict almost as well as the best expert. Typical good forecasters maintain one weight per expert, update these weights depending on the past performances, and output at each step the corresponding weighted linear combination of experts' advices.
The difference between the cumulative prediction error of the forecaster and the one of the best expert is called the regret. The game consists here of upper bounding the regret by a quantity as small as possible.