This paper studies the strongly-convex-strongly-concave minimax optimization with unbalanced dimensionality. Such problems contain several popular applications in data science such as few shot learning and fairness-aware machine learning task. The design of conventional iterative algorithm for minimax optimization typically focuses on reducing the total number of oracle calls, which ignores the unbalanced computational cost for accessing the information from two different variables in minimax. We propose a novel second-order optimization algorithm, called Partial-Quasi-Newton (PQN) method, which takes the advantage of unbalanced structure in the problem to establish the Hessian estimate efficiently. We theoretically prove our PQN method converges to the saddle point faster than existing minimax optimization algorithms. The numerical experiments on real-world applications show the proposed PQN performs significantly better than the state-of-the-art methods.

The original design of Graph Convolution Network (GCN) couples feature transformation and neighborhood aggregation for node representation learning. Recently, some work shows that coupling is inferior to decoupling, which supports deep graph propagation better and has become the latest paradigm of GCN (e.g., APPNP [16] and SGCN [32]). Despite effectiveness, the working mechanisms of the decoupled GCN are not well understood.