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.

翻译：本研究的主要目标是探究模型无关元学习（MAML）在线性系统二次最优控制（LQR）中的局部收敛特性。MAML及其变体已成为在回归、分类和强化学习等领域通过利用先前学习知识快速适应新任务的流行技术。然而，由于非凸性及其结构，其理论保证仍不明确，这在动态系统环境下进一步增加了确保稳定性的难度。本文重点探索LQR环境下的MAML，在保持动态系统稳定性的同时，为其局部收敛性提供理论保证。此外，本文还通过简单的数值结果展示了MAML在LQR任务中的收敛特性。