Consistent Multitask Learning with Nonlinear Output Relations

Key to multitask learning is exploiting the relationships between different tasks inorder to improve prediction performance. Most previous methods have focused onthe case where tasks relations can be modeled as linear operators and regularizationapproaches can be used successfully. However, in practice assuming the tasks tobe linearly related is often restrictive, and allowing for nonlinear structures is achallenge. In this paper, we tackle this issue by casting the problem within theframework of structured prediction. Our main contribution is a novel algorithm forlearning multiple tasks which are related by a system of nonlinear equations thattheir joint outputs need to satisfy. We show that our algorithm can be efficientlyimplemented and study its generalization properties, proving universal consistencyand learning rates. Our theoretical analysis highlights the benefits of non-linearmultitask learning over learning the tasks independently. Encouraging experimentalresults show the benefits of the proposed method in practice.