  Multi-task learning is a framework that enforces different learning tasks to
share their knowledge to improve their generalization performance. It is a hot
and active domain that strives to handle several core issues; particularly,
which tasks are correlated and similar, and how to share the knowledge among
correlated tasks. Existing works usually do not distinguish the polarity and
magnitude of feature weights and commonly rely on linear correlation, due to
three major technical challenges in: 1) optimizing the models that regularize
feature weight polarity, 2) deciding whether to regularize sign or magnitude,
3) identifying which tasks should share their sign and/or magnitude patterns.
To address them, this paper proposes a new multi-task learning framework that
can regularize feature weight signs across tasks. We innovatively formulate it
as a biconvex inequality constrained optimization with slacks and propose a new
efficient algorithm for the optimization with theoretical guarantees on
generalization performance and convergence. Extensive experiments on multiple
datasets demonstrate the proposed methods' effectiveness, efficiency, and
reasonableness of the regularized feature weighted patterns.
