We present a multi-task learning approach to jointly estimate the means of
multiple independent data sets. The proposed multi-task averaging (MTA) algorithm results
in a convex
combination of the single-task maximum likelihood estimates. We derive the
optimal minimum risk estimator and the minimax estimator, and show that these estimators
can be
efficiently estimated. Simulations and real data experiments illustrate the
advantage of
MTA over standard averaging and James-Stein estimation.