  Traditionally, Multi-task Learning (MTL) models optimize the average of
task-related objective functions, which is an intuitive approach and which we
will be referring to as Average MTL. However, a more general framework,
referred to as Conic MTL, can be formulated by considering conic combinations
of the objective functions instead; in this framework, Average MTL arises as a
special case, when all combination coefficients equal 1. Although the advantage
of Conic MTL over Average MTL has been shown experimentally in previous works,
no theoretical justification has been provided to date. In this paper, we
derive a generalization bound for the Conic MTL method, and demonstrate that
the tightest bound is not necessarily achieved, when all combination
coefficients equal 1; hence, Average MTL may not always be the optimal choice,
and it is important to consider Conic MTL. As a byproduct of the generalization
bound, it also theoretically explains the good experimental results of previous
relevant works. Finally, we propose a new Conic MTL model, whose conic
combination coefficients minimize the generalization bound, instead of choosing
them heuristically as has been done in previous methods. The rationale and
advantage of our model is demonstrated and verified via a series of experiments
by comparing with several other methods.
