PMF-CL: Pareto-Minimal-Forgetting Continual Learner for Conflicting Tasks

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.

FSL-SAGE: Accelerating Federated Split Learning via Smashed Activation Gradient Estimation

Collaborative training methods like Federated Learning (FL) and Split Learning (SL) enable distributed machine learning without sharing raw data. However, FL assumes clients can train entire models, which is infeasible for large-scale models. In contrast, while SL alleviates the client memory constraint in FL by offloading most training to the server, it increases network latency due to its sequential nature. Other methods address the conundrum by using local loss functions for parallel client-side training to improve efficiency, but they lack server feedback and potentially suffer poor accuracy. We propose FSL-SAGE (Federated Split Learning via Smashed Activation Gradient Estimation), a new federated split learning algorithm that estimates server-side gradient feedback via auxiliary models. These auxiliary models periodically adapt to emulate server behavior on local datasets. We show that FSL-SAGE achieves a convergence rate of $\mathcal{O}(1/\sqrt{T})$, where $T$ is the number of communication rounds. This result matches FedAvg, while significantly reducing communication costs and client memory requirements. Our empirical results also verify that it outperforms existing state-of-the-art FSL methods, offering both communication efficiency and accuracy.