We present a new accelerated stochastic second-order method that is robust to both
gradient and Hessian inexactness, which occurs typically in machine learning. We establish …

We study stochastic second-order methods for solving general non-convex optimization
problems. We propose using a special version of momentum to stabilize the stochastic …

The optimistic gradient method is useful in addressing minimax optimization problems.
Motivated by the observation that the conventional stochastic version suffers from the need …

Despite the impressive numerical performance of the quasi-Newton and Anderson/nonlinear
acceleration methods, their global convergence rates have remained elusive for over 50 …

In this paper, we propose Cubic Regularized Quasi-Newton Methods for (strongly)
starconvex and Accelerated Cubic Regularized Quasi-Newton for convex optimization. The …

This paper studies second-order methods for convex-concave minimax optimization.
Monteiro and Svaiter (2012) proposed a method to solve the problem with an optimal …

Second-order methods for convex optimization outperform first-order methods in terms of
theoretical iteration convergence, achieving rates up to $ O (k^{-5}) $ for highly-smooth …

In this paper, we investigate the challenging framework of Byzantine-robust training in
distributed machine learning (ML) systems, focusing on enhancing both efficiency and …

In this paper, we investigate the convergence behavior of the Accelerated Newton Proximal
Extragradient (A-NPE) method when employing inexact Hessian information. The exact A …

Variational inequalities represent a broad class of problems, including minimization and min-
max problems, commonly found in machine learning. Existing second-order and high-order …