Recovery Guarantees for Continual Learning of Dependent Tasks: Memory, Data-Dependent Regularization, and Data-Dependent Weights

TL;DR

This paper develops theoretical recovery guarantees for continual learning models with dependent tasks, addressing the challenge of data distribution variation across tasks.

Contribution

It introduces a model for task dependency and provides the first informative bounds for several continual learning paradigms under this model.

Findings

Proves statistical recovery bounds for experience replay with data-independent regularization.

Provides bounds for replay with data-dependent weights.

Establishes guarantees for continual learning with data-dependent regularization.

Abstract

Continual learning (CL) is concerned with learning multiple tasks sequentially without forgetting previously learned tasks. Despite substantial empirical advances over recent years, the theoretical development of CL remains in its infancy. At the heart of developing CL theory lies the challenge that the data distribution varies across tasks, and we argue that properly addressing this challenge requires understanding this variation--dependency among tasks. To explicitly model task dependency, we consider nonlinear regression tasks and propose the assumption that these tasks are dependent in such a way that the data of the current task is a nonlinear transformation of previous data. With this model and under natural assumptions, we prove statistical recovery guarantees (more specifically, bounds on estimation errors) for several CL paradigms in practical use, including experience replay with data-independent regularization and data-independent weights that balance the losses of tasks, replay with data-dependent weights, and continual learning with data-dependent regularization (e.g., knowledge distillation). To the best of our knowledge, our bounds are informative in cases where prior work gives vacuous bounds.