PMF-CL: Pareto-Minimal-Forgetting Continual Learner for Conflicting Tasks

TL;DR

This paper introduces PMF-CL, a continual learning framework that finds Pareto-optimal solutions to minimize forgetting across conflicting tasks, applicable to various regression and classification models.

Contribution

It develops Pareto-minimal-forgetting algorithms for linear and basis-function regression, providing a systematic, memory-efficient approach to continual learning of conflicting tasks.

Findings

Derives Pareto-minimal-forgetting algorithms for multiple models.

Provides memory-efficient iterative updates for quadratic problems.

Addresses the challenge of conflicting tasks in continual learning.

Abstract

In the literature, many continual learning (CL) algorithms have been proposed to address the issue of catastrophic forgetting in ML models (i.e., learning new tasks leads to the loss of performance on previously learned tasks). Although all CL approaches use some form of memory to retain information about past tasks, a grounded understanding of what information needs to be stored to minimize catastrophic forgetting remains elusive. Recently, it has been recognized that under the strong assumption of the existence of a common global minimizer over all tasks, catastrophic forgetting can be completely avoided. However, in practice, tasks rarely have a common global minimizer, and a certain amount of forgetting is inevitable. In this paper, we propose a foundational framework for principled and systematic CL of conflicting tasks using a multi-task learning (MTL) perspective. The approach is based on finding Pareto-optimal solutions, i.e., the solutions which, by definition, minimally forget the previous tasks in the Pareto sense. We derive Pareto-minimal-forgetting CL algorithms for linear and basis-function regression, and general loss functions which have a quadratic upper bound, e.g., logistic regression. For quadratic problems, PMF-CL uses memory-efficient iterative updates with a static memory footage of $\mathcal{O}(d^2)$ for models with $d$ parameters.