在图序列上持续学习——动力系统方法
Learning Continually on a Sequence of Graphs -- The Dynamical System Way
AI总结：
针对非欧几里得图数据的持续学习研究匮乏的问题，提出自适应动态规划视角，将泛化与遗忘构建为双人序贯博弈，证明解的存在与收敛性，在多图基准上取得最优性能。
摘要：
持续学习（Continual Learning，CL）是研究学习一系列相互关联任务的领域，这些任务通常以回归或分类的形式定义。近年来，当这些任务基于欧几里得数据（即图像这类可通过n维实空间中的一组向量描述的数据）定义时，持续学习已得到广泛研究。然而，当持续学习任务对应的数据为非欧几里得数据（即图、点云或流形这类欧几里得度量下的相似性概念不成立的数据）时，相关文献相当稀少。例如，图由顶点和边的元组描述，两个图之间的相似性无法通过欧几里得度量良好定义。由于数据的这一基本特性，为非欧几里得数据开发持续学习方法面临若干理论和方法层面的挑战。具体而言，面向图的持续学习需要显式建模顶点和边的非平稳行为及其对学习问题的影响。因此，在本工作中，我们为面向图的持续学习提出了一种自适应动态规划视角。我们将学习新任务（泛化）与记住先前学习的任务（遗忘）这两种行为构建为一个双人序贯博弈。我们从数学上证明了该博弈解的存在性，并论证了向博弈解的收敛性。最后，我们在多个图基准数据集上通过全面的消融实验验证了所提方法的有效性，同时取得了当前最优（state-of-the-art）性能。
英文摘要：
Continual learning~(CL) is a field concerned with learning a series of inter-related task with the tasks typically defined in the sense of either regression or classification. In recent years, CL has been studied extensively when these tasks are defined using Euclidean data -- data, such as images, that can be described by a set of vectors in an n-dimensional real space. However, the literature is quite sparse, when the data corresponding to a CL task is nonEuclidean -- data , such as graphs, point clouds or manifold, where the notion of similarity in the sense of Euclidean metric does not hold. For instance, a graph is described by a tuple of vertices and edges and similarities between two graphs is not well defined through a Euclidean metric. Due to this fundamental nature of the data, developing CL for nonEuclidean data presents several theoretical and methodological challenges. In particular, CL for graphs requires explicit modelling of nonstationary behavior of vertices and edges and their effects on the learning problem. Therefore, in this work, we develop a adaptive dynamic programming viewpoint for CL with graphs. In this work, we formulate a two-player sequential game between the act of learning new tasks~(generalization) and remembering previously learned tasks~(forgetting). We prove mathematically the existence of a solution to the game and demonstrate convergence to the solution of the game. Finally, we demonstrate the efficacy of our method on a number of graph benchmarks with a comprehensive ablation study while establishing state-of-the-art performance.
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