Online Learning Guided Curvature Approximation: A Quasi-Newton Method with Global Non-Asymptotic Superlinear Convergence

no code implementations • 16 Feb 2023 • Ruichen Jiang, Qiujiang Jin, Aryan Mokhtari

Quasi-Newton algorithms are among the most popular iterative methods for solving unconstrained minimization problems, largely due to their favorable superlinear convergence property.

Exploiting Local Convergence of Quasi-Newton Methods Globally: Adaptive Sample Size Approach

no code implementations • NeurIPS 2021 • Qiujiang Jin, Aryan Mokhtari

In this paper, we use an adaptive sample size scheme that exploits the superlinear convergence of quasi-Newton methods globally and throughout the entire learning process.

Non-asymptotic Superlinear Convergence of Standard Quasi-Newton Methods

no code implementations • 30 Mar 2020 • Qiujiang Jin, Aryan Mokhtari

In this paper, we provide a finite-time (non-asymptotic) convergence analysis for Broyden quasi-Newton algorithms under the assumptions that the objective function is strongly convex, its gradient is Lipschitz continuous, and its Hessian is Lipschitz continuous at the optimal solution.