SCORE: Approximating Curvature Information under Self-Concordant Regularization

In this paper, we propose the SCORE (self-concordant regularization) framework for unconstrained minimization problems which incorporates second-order information in the Newton decrement framework for convex optimization. We propose the generalized Gauss-Newton with Self-Concordant Regularization (GGN-SCORE) algorithm that updates the minimization variables each time it receives a new input batch. The proposed algorithm exploits the structure of the second-order information in the Hessian matrix, thereby reducing computational overhead. GGN-SCORE demonstrates how we may speed up convergence while also improving model generalization for problems that involve regularized minimization under the SCORE framework. Numerical experiments show the efficiency of our method and its fast convergence, which compare favorably against baseline first-order and quasi-Newton methods. Additional experiments involving non-convex (overparameterized) neural network training problems show similar convergence behaviour thereby highlighting the promise of the proposed algorithm for non-convex optimization.Comment: 21 pages, 12 figure