Primal Dual Continual Learning: Balancing Stability and Plasticity through Adaptive Memory Allocation

TL;DR

This paper introduces a primal-dual framework for continual learning that explicitly handles constraints, enabling adaptive memory allocation to balance stability and plasticity, and demonstrates its effectiveness on various benchmarks.

Contribution

It formulates continual learning as a constrained optimization problem and uses dual variables for adaptive memory management, a novel approach in this domain.

Findings

Dual variables indicate task difficulty and sample impact.

Adaptive buffer partitioning improves learning stability.

Empirical results validate the approach across benchmarks.

Abstract

Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly. In this work, we show that it is both possible and beneficial to undertake the constrained optimization problem directly. To do this, we leverage recent results in constrained learning through Lagrangian duality. We focus on memory-based methods, where a small subset of samples from previous tasks can be stored in a replay buffer. In this setting, we analyze two versions of the continual learning problem: a coarse approach with constraints at the task level and a fine approach with constraints at the sample level. We show that dual variables indicate the sensitivity of the optimal value of the continual learning problem with respect to constraint perturbations. We then leverage this result to partition the buffer in the coarse approach, allocating more resources to harder tasks, and to populate the buffer in the fine approach, including only impactful samples. We derive a deviation bound on dual variables as sensitivity indicators, and empirically corroborate this result in diverse continual learning benchmarks. We also discuss the limitations of these methods with respect to the amount of memory available and the expressiveness of the parametrization.