Revisiting the Curvature-aided IAG: Improved Theory and Reduced Complexity

The curvature-aided IAG (CIAG) algorithm is an efficient asynchronous optimization method that accelerates IAG using a delay compensation technique. However, existing step-size rules for CIAG are conservative and hard to implement, and the Hessian computation in CIAG is often computationally expensive. To alleviate these issues, we first provide an easy-to-implement and less conservative step-size rule for CIAG. Next, we propose a modified CIAG algorithm that reduces the computational complexity by approximating the Hessian with a constant matrix. Convergence results are derived for each algorithm on both convex and strongly convex problems, and numerical experiments on logistic regression demonstrate their effectiveness in practice.