Decentralized collaborative continual learning: A multi-objective minimization-based technique

Yara Zgheib; Marc Antonini; Roula Nassif

cs.MAOct 7, 2026

Decentralized collaborative continual learning: A multi-objective minimization-based technique

Authors: Yara Zgheib, Marc Antonini, Roula Nassif

Organizations: Universit´e Cˆote d’Azur, I3S Laboratory, CNRS, France

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.

Figures & tables

Panel of Figure 1 — Fig. 1: Continual learning over multi-agent network. (Left) A network of $K$ agents receives a sequence of tasks over time. The objective is for the agents to learn each new task as it arrives while retaining performance on previously learned tasks. (Right) Continual learning block associated with agent $k$ , where memory buffers retain data samples from previously learned tasks (which are replayed to reduce forgetting). Agent $k$ seeks to minimize the multi-objective risk ( 4 ), while simultaneously exploiting information from its neighboring agents $\ell\in\mathcal{N}_{k}$ through the minimization of the global objective in ( 5 ).

\boldsymbol{\psi}_{k,t,i}=\boldsymbol{w}_{k,t,i-1}-\mu\widehat{\nabla_{w}\boldsymbol{J}_{k,t}^{\text{multi}}}(\boldsymbol{w}_{k,t,i-1})

(6)

Algorithm 1 Diffusion ATC-based approach for decentralized continual learning

Panel of Figure 3 — Fig. 2: (Left) Network topology. (Right) Performance of Algorithm 1 w.r.t $\boldsymbol{w}_{t}^{\star}$ , the solution of problem ( 5 ) ( $\mu_{0}=0.0025$ ).

Fig. 3: Benefit of continual learning. (Left) Average MSD across tasks, defined in ( 55 ). (Right) Average forgetting error, defined in ( 70 ).

Fig. 4: Benefit of collaborative continual learning. (Left) Average MSD across tasks, defined in ( 55 ). (Right) Average forgetting error, defined in ( 70 ).

	$\lambda=0$	$\lambda=0.1$	$\lambda=0.9$
Non-collaborative	$61.579\pm 0.032/-6.287\pm 0.041$	$64.498\pm 0.051/-1.909\pm 0.061$	$63.350\pm 0.109/-1.643\pm 0.115$
Collaborative	$62.724\pm 0.035/-10.529\pm 0.044$	$67.841\pm 0.035/-2.048\pm 0.045$	$\boldsymbol{68.569\pm 0.088/-0.313\pm 0.087}$

TABLE 1: ACC/BWT(%) for the collaborative and non-collaborative settings (sampling probability

p_{k,t}=0.2

	$p_{k,t}=0.08$	$p_{k,t}=0.2$	$p_{k,t}=0.4$
Non-collaborative	$62.896\pm 0.118/-3.039\pm 0.126$	$64.018\pm 0.089/-1.837\pm 0.108$	$64.699\pm 0.077/\boldsymbol{-1.125\pm 0.080}$
Collaborative	$67.787\pm 0.095/-1.716\pm 0.106$	$68.288\pm 0.067/-1.256\pm 0.080$	$\boldsymbol{68.485\pm 0.049}/-1.128\pm 0.056$

TABLE 2: ACC/BWT(%) for the collaborative and non-collaborative settings (regularization strength

\lambda=0.5

	$p_{k,t}=0.08$	$p_{k,t}=0.2$	$p_{k,t}=0.4$
Non-collaborative	$61.834\pm 0.119/-3.471\pm 0.125$	$63.350\pm 0.109/-1.643\pm 0.115$	$64.209\pm 0.084/-0.773\pm 0.092$
Collaborative	$67.275\pm 0.129/-1.110\pm 0.125$	$68.569\pm 0.088/-0.313\pm 0.087$	$\boldsymbol{69.164\pm 0.072/0.111\pm 0.066}$

TABLE 3: ACC/BWT(%) for the collaborative and non-collaborative settings (regularization strength

\lambda=0.9

$p_{k,t}$	Memory	Non-collaborative	Collaborative
0.05	Bernoulli	$61.045\pm 0.130/-4.543\pm 0.130$	$66.434\pm 0.153/-1.628\pm 0.163$
0.05	Class-balanced	$62.430\pm 0.152/-2.870\pm 0.157$	$\boldsymbol{66.735\pm 0.136/-1.453\pm 0.123}$
0.40	Bernoulli	$64.230\pm 0.082/-0.801\pm 0.091$	$69.107\pm 0.054/0.104\pm 0.071$
0.40	Class-balanced	$64.302\pm 0.094/-0.680\pm 0.095$	$\boldsymbol{69.192\pm 0.059/0.141\pm 0.071}$

TABLE 4: The impact of memory selection strategies in terms of ACC/BWT(%) for the collaborative and non-collaborative settings (

\lambda=0.9

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In continual learning, the primary challenge is to learn new information without forgetting old knowledge. A common solution addresses this trade-off through regularization, penalizing changes to parameters critical for previous tasks. In most cases, this regularization term is directly added to the training loss and optimized with standard gradient descent, which blends learning and retention signals into a single update and does not explicitly separate essential parameters from redundant ones. As task sequences grow, this coupling can over-constrain the model, limiting forward transfer and leading to inefficient use of capacity. We propose a different approach that separates task learning from stability enforcement via operator splitting. The learning step focuses on minimizing the current task loss, while a proximal stability step applies a sparse regularizer to prune unnecessary parameters and preserve task-relevant ones. This turns the stability-plasticity into a negotiated update between two complementary operators, rather than a conflicting gradient. We provide theoretical justification for the splitting method on the continual-learning objective, and demonstrate that our proposed solver achieves state-of-the-art results on standard benchmarks, improving both stability and adaptability without the need for replay buffers, Bayesian sampling, or meta-learning components.

Abstract

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