# Aggregating Algorithm Regression

Aggregating Algorithm Regression (AAR) is an application of the Aggregating Algorithm to the online linear regression setting (see Vovk (2001)).

For the online linear regression problem with bounded signal , Vovk (2001) proves that for the square-loss function AAR can achieve

,

where is the loss of any linear function of .

The algorithm works as follows (all the vectors are columns):

Initialize vector , and matrix ;
FOR