Jia

Srijith Nair, Atilla Eryilmaz, Jia et al.

In the literature, many continual learning (CL) algorithms have been proposed to address the issue of catastrophic forgetting in ML models (i.e., learning new tasks leads to the loss of performance on previously learned tasks). Although all CL approaches use some form of memory to retain information about past tasks, a grounded understanding of what information needs to be stored to minimize catastrophic forgetting remains elusive. Recently, it has been recognized that under the strong assumption of the existence of a common global minimizer over all tasks, catastrophic forgetting can be completely avoided. However, in practice, tasks rarely have a common global minimizer, and a certain amount of forgetting is inevitable. In this paper, we propose a foundational framework for principled and systematic CL of conflicting tasks using a multi-task learning (MTL) perspective. The approach is based on finding Pareto-optimal solutions, i.e., the solutions which, by definition, minimally forget the previous tasks in the Pareto sense. We derive Pareto-minimal-forgetting CL algorithms for linear and basis-function regression, and general loss functions which have a quadratic upper bound, e.g., logistic regression. For quadratic problems, PMF-CL uses memory-efficient iterative updates with a static memory footage of $\mathcal{O}(d^2)$ for models with $d$ parameters.

Fatemeh, Nourzad, Amirhossein Roknilamouki et al.

Aligning Large Language Models (LLMs) with human values often involves balancing multiple, conflicting objectives such as helpfulness and harmlessness. Training these models is computationally intensive, and centralizing the process raises significant data privacy concerns. Federated Learning (FL) offers a compelling alternative, but existing Federated Multi-Objective Optimization (FMOO) methods face severe communication bottlenecks as their reliance on transmitting multiple gradients to a server is unscalable for large models. We introduce FIRM (Federated In-client Regularized Multi-objective alignment), a novel algorithm that achieves both client disagreement drift mitigation and communication efficiency. In FIRM, each client locally solves a regularized multi-objective optimization problem. By directly mitigating client disagreement drift through in-client regularization, our method eliminates the need for the multi-gradient transmissions common in prior works. Consequently, clients need only to transmit a single set of adapted parameters, maintaining high communication efficiency. We prove that our algorithm converges to Pareto-stationary points and, to our knowledge, provide the first finite-time convergence guarantees for this federated multi-objective alignment setting. Empirically, we show that FIRM leads to smoother training dynamics, reduced client disagreement drift, and improved reward trade-offs compared to baselines. We further propose a method to incorporate a preference over the objectives and report empirical Pareto plots, demonstrating that FIRM can smoothly adapt trade-offs between objectives in response to specified preferences.