首次在非独立同分布数据下证明持续学习的全局收敛性。
Global Convergence of Continual Learning on Non-IID Data
- 用随机李雅普诺夫函数和鞅估计方法分析回归模型持续学习。
- 无需特征激励条件，给出遗忘与遗憾的收敛速率。
- 适合研究持续学习理论或非IID数据场景的学者。
持续学习旨在顺序学习多个任务，近年来受到广泛关注。然而，现有研究多集中于经验分析，理论研究仍不充分。近期少数工作仅针对线性回归，依赖严格的独立同分布假设及难以验证的特征数据持久激励条件。为克服这一根本局限，本文首次对回归模型的持续学习提供了一般且全面的理论分析。通过引入随机李雅普诺夫函数与鞅估计技术，我们在一般数据条件下建立了持续学习几乎必然收敛的结果。此外，无需任何激励假设，本文还给出了遗忘与遗憾指标的收敛速率。
原文摘要 · Abstract (English)
Continual learning, which aims to learn multiple tasks sequentially, has gained extensive attention. However, most existing work focuses on empirical studies, and the theoretical aspect remains under-explored. Recently, a few investigations have considered the theory of continual learning only for linear regressions, establishes the results based on the strict independent and identically distributed (i.i.d.) assumption and the persistent excitation on the feature data that may be difficult to verify or guarantee in practice. To overcome this fundamental limitation, in this paper, we provide a general and comprehensive theoretical analysis for continual learning of regression models. By utilizing the stochastic Lyapunov function and martingale estimation techniques, we establish the almost sure convergence results of continual learning under a general data condition for the first time. Additionally, without any excitation condition imposed on the data, the convergence rates for the forgetting and regret metrics are provided.
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