  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 demonstrate that MTA estimators often
outperform both single-task and James-Stein estimators.
