arXiv:2610.10882v1 Announce Type: new Abstract: In this work, we formulate decentralized continual learning within a multi-objective optimization framework. For a given inference task t (corresponding to a common minimizer shared by the cost functions of all agents), agents collecting data in a distributed and streamed manner are only allowed to perform local computations and to exchange information with neighboring agents over the underlying communication graph. As tasks evolve sequentially over time, agents must adapt to newly arriving tasks while retaining knowledge acquired from previously learned ones. This requirement leads to the wellknown stability plasticity dilemma, where stability refers to the ability to retain previous knowledge, while plasticity refers to the ability to learn and adapt to new tasks. To address the stability challenge, agents store subsets of samples from past tasks in local memory buffers. Then, through an appropriate multiobjective formulation, the stored information is incorporated into the learning process so that parameter updates account jointly for the current task and previously learned tasks. The proposed decentralized continual learning approach is analyzed in the mean square error sense under general assumptions on the individual cost functions and gradient noise processes. The analysis reveals that cooperation among agents improves the performance of continual learning. In particular, by exchanging information with neighboring agents, decentralized collaborative learning can exploit the diversity of locally observed data and memory buffers to improve the network average mean-square deviation (MSD) across tasks. Finally, simulations illustrate the theoretical findings and the effectiveness of the method in reducing forgetting and improving the average MSD across tasks.