Asymptotic Behavior of Multi--Task Learning: Implicit Regularization and Double Descent Effects

TL;DR

This paper provides an asymptotic analysis of multi-task learning, revealing how combining related tasks acts as implicit regularization, improves generalization, and delays the double descent phenomenon.

Contribution

It offers a precise asymptotic explanation for the benefits of multi-task learning and empirically demonstrates its effect on generalization and double descent.

Findings

Combining tasks is asymptotically equivalent to regularized models.

Multi-task learning delays the double descent phenomenon.

Empirical results confirm improved generalization with task combination.

Abstract

Multi--task learning seeks to improve the generalization error by leveraging the common information shared by multiple related tasks. One challenge in multi--task learning is identifying formulations capable of uncovering the common information shared between different but related tasks. This paper provides a precise asymptotic analysis of a popular multi--task formulation associated with misspecified perceptron learning models. The main contribution of this paper is to precisely determine the reasons behind the benefits gained from combining multiple related tasks. Specifically, we show that combining multiple tasks is asymptotically equivalent to a traditional formulation with additional regularization terms that help improve the generalization performance. Another contribution is to empirically study the impact of combining tasks on the generalization error. In particular, we empirically show that the combination of multiple tasks postpones the double descent phenomenon and can mitigate it asymptotically.