Theory for group-robust continual learning

To support the continuous adaptation of agentic AI systems as new task data arrives, continual learning (CL) has become increasingly important. However, rehearsal-based methods, a dominant class of approaches in CL, typically treat all past tasks equally to mitigate catastrophic forgetting. In this paper, we prove that this practice can destabilize learning by causing poor retention of knowledge from rare or difficult task groups in terms of large excess risk. Accordingly, we develop group-robust continual learning (GRCL), a new framework for achieving stable and robust performance across task groups, with a particular focus on improving the worst-group performance. We design two rehearsal-based GRCL methods guided by excess risk bounds: group-balanced replay allocates memory uniformly across groups to minimize a simplified bound, while difficulty-adaptive replay incorporates group learning difficulty estimated during CL into its replay buffer allocation and minimizes a tighter, difficulty-aware bound. We further extend GRCL to the setting where group information is unknown throughout CL. In this case, we propose two group identification methods based on maximum mean discrepancy and online expectation-maximization, respectively, and establish theoretical guarantees for their identification performance. We also derive a small excess-risk bound for GRCL using the estimated group identities. Experiments on real-world datasets show that our rehearsal-based GRCL methods significantly improve robustness over classicalbaselines by enhancing worst-group performance.