Statistical Theory of Multi-stage Newton Iteration Algorithm for Online Continual Learning

TL;DR

This paper introduces a statistical framework and a multi-step Newton iteration algorithm for online continual learning, effectively addressing catastrophic forgetting in non-stationary data streams with theoretical guarantees and empirical validation.

Contribution

It proposes a novel statistical approach with a multi-step Newton algorithm that reduces computational costs and provides asymptotic normality for inference in continual learning.

Findings

Effective mitigation of catastrophic forgetting.

Reduced computational complexity in streaming data processing.

Validated performance on synthetic and real datasets.

Abstract

We focus on the critical challenge of handling non-stationary data streams in online continual learning environments, where constrained storage capacity prevents complete retention of historical data, leading to catastrophic forgetting during sequential task training. To more effectively analyze and address the problem of catastrophic forgetting in continual learning, we propose a novel continual learning framework from a statistical perspective. Our approach incorporates random effects across all model parameters and allows the dimension of parameters to diverge to infinity, offering a general formulation for continual learning problems. To efficiently process streaming data, we develop a Multi-step Newton Iteration algorithm that significantly reduces computational costs in certain scenarios by alleviating the burden of matrix inversion. Theoretically, we derive the asymptotic normality of the estimator, enabling subsequent statistical inference. Comprehensive validation through synthetic data experiments and two real datasets analyses demonstrates the effectiveness of our proposed method.