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Continual learning~(CL) is a field concerned with learning a series ofinter-related task with the tasks typically defined in the sense of eitherregression or classification. In recent years, CL has been studied extensivelywhen these tasks are defined using Euclidean data -- data, such as images, thatcan 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 isnonEuclidean -- data , such as graphs, point clouds or manifold, where thenotion of similarity in the sense of Euclidean metric does not hold. Forinstance, a graph is described by a tuple of vertices and edges andsimilarities between two graphs is not well defined through a Euclidean metric.Due to this fundamental nature of the data, developing CL for nonEuclidean datapresents several theoretical and methodological challenges. In particular, CLfor graphs requires explicit modelling of nonstationary behavior of verticesand edges and their effects on the learning problem. Therefore, in this work,we develop a adaptive dynamic programming viewpoint for CL with graphs. In thiswork, we formulate a two-player sequential game between the act of learning newtasks~(generalization) and remembering previously learned tasks~(forgetting).We prove mathematically the existence of a solution to the game and demonstrateconvergence to the solution of the game. Finally, we demonstrate the efficacyof our method on a number of graph benchmarks with a comprehensive ablationstudy while establishing state-of-the-art performance.

Learning Continually on a Sequence of Graphs -- The Dynamical System Way