Tri-Level Navigator: LLM-Empowered Tri-Level Learning for Time Series OOD Generalization

TL;DR

This paper introduces a tri-level learning framework using large language models to improve out-of-distribution generalization in time series data, with theoretical guarantees and empirical validation.

Contribution

It proposes a novel tri-level learning framework for time series OOD generalization and develops a stratified localization algorithm with convergence guarantees.

Findings

Effective OOD generalization on real-world datasets.

Theoretical proof of algorithm convergence.

Iteration complexity is bounded by O(1/ε²).

Abstract

Out-of-Distribution (OOD) generalization in machine learning is a burgeoning area of study. Its primary goal is to enhance the adaptability and resilience of machine learning models when faced with new, unseen, and potentially adversarial data that significantly diverges from their original training datasets. In this paper, we investigate time series OOD generalization via pre-trained Large Language Models (LLMs). We first propose a novel \textbf{T}ri-level learning framework for \textbf{T}ime \textbf{S}eries \textbf{O}OD generalization, termed TTSO, which considers both sample-level and group-level uncertainties. This formula offers a fresh theoretic perspective for formulating and analyzing OOD generalization problem. In addition, we provide a theoretical analysis to justify this method is well motivated. We then develop a stratified localization algorithm tailored for this tri-level optimization problem, theoretically demonstrating the guaranteed convergence of the proposed algorithm. Our analysis also reveals that the iteration complexity to obtain an $\epsilon$-stationary point is bounded by O($\frac{1}{\epsilon^{2}}$). Extensive experiments on real-world datasets have been conducted to elucidate the effectiveness of the proposed method.