Convergence of Gradient-based MAML in LQR

TL;DR

This paper analyzes the local convergence properties of gradient-based MAML in linear quadratic control, providing theoretical guarantees and demonstrating stability and convergence through numerical experiments.

Contribution

It offers the first local convergence guarantees for MAML in LQR, ensuring stability in dynamic systems, which was previously unestablished.

Findings

MAML converges locally in LQR tasks under certain conditions.

Theoretical guarantees ensure stability of the control system.

Numerical results confirm convergence behavior.

Abstract

The main objective of this research paper is to investigate the local convergence characteristics of Model-agnostic Meta-learning (MAML) when applied to linear system quadratic optimal control (LQR). MAML and its variations have become popular techniques for quickly adapting to new tasks by leveraging previous learning knowledge in areas like regression, classification, and reinforcement learning. However, its theoretical guarantees remain unknown due to non-convexity and its structure, making it even more challenging to ensure stability in the dynamic system setting. This study focuses on exploring MAML in the LQR setting, providing its local convergence guarantees while maintaining the stability of the dynamical system. The paper also presents simple numerical results to demonstrate the convergence properties of MAML in LQR tasks.