原始对偶持续学习：通过自适应记忆分配平衡稳定性与可塑性
Primal Dual Continual Learning: Balancing Stability and Plasticity through Adaptive Memory Allocation
AI总结：
本文将持续学习视为受约束优化问题，利用拉格朗日对偶性分析任务级与样本级约束，通过对偶变量指示的敏感性自适应分配重放缓冲区资源，在多个基准上验证了有效性并讨论了其局限性。
摘要：
持续学习本质上是一个受约束的学习问题。其目标是在无遗忘要求下学习一个预测器。尽管先前有几项研究如此表述，但它们并未显式解决这一受约束问题。在本研究中，我们表明直接处理该受约束优化问题是可能且有益的。为此，我们利用了通过拉格朗日对偶性进行受约束学习的最新成果。我们关注基于记忆的方法，其中先前任务的一小部分样本可存储在重放缓冲区中。在此设定下，我们分析了持续学习问题的两个版本：在任务层面施加约束的粗粒度方法，以及在样本层面施加约束的细粒度方法。我们证明对偶变量指示了持续学习问题最优值对约束扰动的敏感性。随后我们利用这一结果在粗粒度方法中对缓冲区进行划分，将更多资源分配给更难的任务；并在细粒度方法中填充缓冲区，仅包含有影响力的样本。我们推导了作为敏感性指标的对偶变量偏差界，并在多样化的持续学习基准上实证证实了该结果。我们还讨论了这些方法在可用记忆量和参数化表达能力方面的局限性。
英文摘要：
Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly. In this work, we show that it is both possible and beneficial to undertake the constrained optimization problem directly. To do this, we leverage recent results in constrained learning through Lagrangian duality. We focus on memory-based methods, where a small subset of samples from previous tasks can be stored in a replay buffer. In this setting, we analyze two versions of the continual learning problem: a coarse approach with constraints at the task level and a fine approach with constraints at the sample level. We show that dual variables indicate the sensitivity of the optimal value of the continual learning problem with respect to constraint perturbations. We then leverage this result to partition the buffer in the coarse approach, allocating more resources to harder tasks, and to populate the buffer in the fine approach, including only impactful samples. We derive a deviation bound on dual variables as sensitivity indicators, and empirically corroborate this result in diverse continual learning benchmarks. We also discuss the limitations of these methods with respect to the amount of memory available and the expressiveness of the parametrization.
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