Online Multi-task Learning with Hard Constraints

TL;DR

This paper introduces an efficient online multi-task learning framework with constraints, enabling simultaneous decision-making across related tasks while satisfying specific restrictions, and extends the model to various complex scenarios.

Contribution

It proposes a tractable approach for constrained multi-task online learning, reducing the problem to an online shortest path computation, and extends the model to complex settings.

Findings

Efficient algorithms for constrained multi-task online learning.

Extension to tracking, bandit, and infinite task scenarios.

Reduction of constrained decision-making to shortest path problems.

Abstract

We discuss multi-task online learning when a decision maker has to deal simultaneously with M tasks. The tasks are related, which is modeled by imposing that the M-tuple of actions taken by the decision maker needs to satisfy certain constraints. We give natural examples of such restrictions and then discuss a general class of tractable constraints, for which we introduce computationally efficient ways of selecting actions, essentially by reducing to an on-line shortest path problem. We briefly discuss "tracking" and "bandit" versions of the problem and extend the model in various ways, including non-additive global losses and uncountably infinite sets of tasks.