Learning Continually on a Sequence of Graphs -- The Dynamical System Way
Krishnan Raghavan Prasanna Balaprakash
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.