PMF-CL: 面向冲突任务的帕累托最小遗忘持续学习器
PMF-CL: Pareto-Minimal-Forgetting Continual Learner for Conflicting Tasks
AI总结：
提出基于多任务学习视角的帕累托最优框架，通过寻找帕累托最优解实现冲突任务下最小化遗忘的持续学习，并推导出适用于线性回归、基函数回归及具有二次上界损失函数的帕累托最小遗忘算法。
摘要：
文献中提出了许多持续学习算法来解决机器学习模型中的灾难性遗忘问题（即学习新任务导致先前学习任务性能下降）。尽管所有持续学习方法都使用某种形式的记忆来保留过去任务的信息，但对需要存储哪些信息以最小化灾难性遗忘的基本理解仍然难以捉摸。最近，人们认识到，在存在所有任务共同全局最小化器的强假设下，灾难性遗忘可以完全避免。然而，在实践中，任务很少具有共同的全局最小化器，一定程度的遗忘是不可避免的。本文提出了一个基于多任务学习视角的、原则性且系统化的冲突任务持续学习基础框架。该方法基于寻找帕累托最优解，即根据定义，在帕累托意义上最小化遗忘先前任务的解。我们推导了线性回归和基函数回归的帕累托最小遗忘持续学习算法，以及具有二次上界的一般损失函数（例如逻辑回归）。对于二次问题，PMF-CL使用内存高效的迭代更新，对于具有$d$个参数的模型，静态内存占用为$\mathcal{O}(d^2)$。
英文摘要：
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 reframing of CL as balancing conflicting tasks in hindsight from 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 a Pareto-minimal-forgetting CL (PMF-CL) algorithm for linear and basis-function regression. Our algorithm naturally extends to loss functions with quadratic upper bounds around their minimizers, despite consuming only a static memory footprint of $O(d^2)$ for $d$ model parameters, independent of the number of sequentially occurring tasks $T$. In the quadratic-loss setting, we obtain exact hindsight Pareto-optimal guarantees on forgetting. In the quadratic-upper-bound setting, forgetting is provably bounded, with the tightness of the forgetting bound being directly determined by the tightness of the quadratic bound on the loss function. Our numerical results validate our theoretical claims of convergence to the Pareto-optimal solution, and demonstrate that we consistently out-perform prior empirical methods while occupying lesser memory.
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