Theoretical Investigations and Practical Enhancements on Tail Task Risk Minimization in Meta Learning

TL;DR

This paper provides a theoretical framework and practical improvements for tail task risk minimization in meta learning, enhancing robustness in large models through a max-min optimization approach and equilibrium analysis.

Contribution

It introduces a Stackelberg equilibrium-based approach, derives generalization bounds, and demonstrates scalability and robustness improvements in large multimodal models.

Findings

Theoretical reduction to max-min optimization problem.

Establishment of Stackelberg equilibrium as the solution.

Empirical validation shows improved robustness and scalability.

Abstract

Meta learning is a promising paradigm in the era of large models and task distributional robustness has become an indispensable consideration in real-world scenarios. Recent advances have examined the effectiveness of tail task risk minimization in fast adaptation robustness improvement \citep{wang2023simple}. This work contributes to more theoretical investigations and practical enhancements in the field. Specifically, we reduce the distributionally robust strategy to a max-min optimization problem, constitute the Stackelberg equilibrium as the solution concept, and estimate the convergence rate. In the presence of tail risk, we further derive the generalization bound, establish connections with estimated quantiles, and practically improve the studied strategy. Accordingly, extensive evaluations demonstrate the significance of our proposal and its scalability to multimodal large models in boosting robustness.