Theoretical Foundations of Continual Learning via Drift-Plus-Penalty

2026-06-07

AI Summary

This work addresses catastrophic forgetting in continual learning under non-stationary data streams by proposing the COLD framework, which introduces, for the first time, the Drift-Plus-Penalty stochastic optimization method from control theory into this domain. COLD formulates forgetting as a controlled dynamic process, employing virtual queues to track performance deviations on historical tasks and jointly minimizing the current task loss and queue drift at each optimization step. This mechanism explicitly governs the stability-plasticity trade-off. The framework provides theoretical guarantees on stability and convergence, and achieves significantly superior performance over state-of-the-art methods on standard benchmarks, enabling controllable and efficient suppression of catastrophic forgetting.

Abstract

In many real-world settings, data streams are nonstationary and arrive sequentially, requiring learning systems to adapt continuously without retraining from scratch. Continual learning (CL) addresses this challenge by incorporating new tasks while mitigating catastrophic forgetting, where learning new information degrades performance on previously acquired knowledge. We introduce a control-theoretic perspective on CL that explicitly regulates the evolution of forgetting, framing adaptation as a controlled process subject to long-term stability constraints. We focus on replay-based CL, where a finite memory buffer stores representative samples from prior tasks. We propose COntinual Learning with Drift-Plus-Penalty (COLD), a continual learning framework based on the Drift-Plus-Penalty (DPP) principle from stochastic optimization. To facilitate analysis, we also consider an oracle variant, COLD-ORACLE, as a reference benchmark. At each task, both methods minimize the current task loss while maintaining a virtual queue that tracks deviations from long-term stability on previously learned tasks, capturing the stability-plasticity trade-off as a regulated dynamical process. We establish stability and convergence guarantees that characterize this trade-off through a tunable control parameter. Experiments on standard benchmarks demonstrate that COLD consistently outperforms a broad range of state-of-the-art CL methods while providing competitive and controllable forgetting behavior through explicit regulation of stability and plasticity.

Problem

• continual learning
• catastrophic forgetting
• nonstationary data streams
• stability-plasticity trade-off

Innovation

• Continual Learning
• Drift-Plus-Penalty
• Stability-Plasticity Trade-off
• Control-Theoretic Framework
• Catastrophic Forgetting