Understanding Benign Overfitting in Gradient-Based Meta Learning

TL;DR

This paper investigates why overparameterized gradient-based meta learning models, especially in bilevel linear regression settings, generalize well despite overfitting tendencies, by analyzing the interplay of data heterogeneity and model adaptation.

Contribution

It provides a theoretical analysis of benign overfitting in gradient-based meta learning with overparameterized linear models, highlighting the roles of data heterogeneity and model adaptation.

Findings

Overparameterized models can generalize well in meta learning.

Data heterogeneity influences the generalization performance.

Numerical simulations support the theoretical analysis.

Abstract

Meta learning has demonstrated tremendous success in few-shot learning with limited supervised data. In those settings, the meta model is usually overparameterized. While the conventional statistical learning theory suggests that overparameterized models tend to overfit, empirical evidence reveals that overparameterized meta learning methods still work well -- a phenomenon often called "benign overfitting." To understand this phenomenon, we focus on the meta learning settings with a challenging bilevel structure that we term the gradient-based meta learning, and analyze its generalization performance under an overparameterized meta linear regression model. While our analysis uses the relatively tractable linear models, our theory contributes to understanding the delicate interplay among data heterogeneity, model adaptation and benign overfitting in gradient-based meta learning tasks. We corroborate our theoretical claims through numerical simulations.