Convex Learning of Multiple Tasks and their Structure

TL;DR

This paper introduces a convex optimization framework for multi-task learning that efficiently incorporates prior knowledge of task structure, enabling the learning of tasks and their relationships with proven convergence guarantees.

Contribution

It presents a unified convex approach to encode task structure in multi-task learning, generalizing existing methods and ensuring global convergence with block coordinate algorithms.

Findings

Framework recovers existing methods as special cases

Convex optimization approach guarantees convergence to global minimum

Efficient algorithms for learning task structure and relationships

Abstract

Reducing the amount of human supervision is a key problem in machine learning and a natural approach is that of exploiting the relations (structure) among different tasks. This is the idea at the core of multi-task learning. In this context a fundamental question is how to incorporate the tasks structure in the learning problem.We tackle this question by studying a general computational framework that allows to encode a-priori knowledge of the tasks structure in the form of a convex penalty; in this setting a variety of previously proposed methods can be recovered as special cases, including linear and non-linear approaches. Within this framework, we show that tasks and their structure can be efficiently learned considering a convex optimization problem that can be approached by means of block coordinate methods such as alternating minimization and for which we prove convergence to the global minimum.