Related papers: Deep Reinforcement Learning via L-BFGS Optimizatio…
Deep learning algorithms often require solving a highly non-linear and nonconvex unconstrained optimization problem. Methods for solving optimization problems in large-scale machine learning, such as deep learning and deep reinforcement…
While first-order methods are popular for solving optimization problems that arise in large-scale deep learning problems, they come with some acute deficiencies. To diminish such shortcomings, there has been recent interest in applying…
Stochastic gradient descent and other first-order variants, such as Adam and AdaGrad, are commonly used in the field of deep learning due to their computational efficiency and low-storage memory requirements. However, these methods do not…
Machine learning (ML) problems are often posed as highly nonlinear and nonconvex unconstrained optimization problems. Methods for solving ML problems based on stochastic gradient descent are easily scaled for very large problems but may…
Global convergence of an online (stochastic) limited memory version of the Broyden-Fletcher- Goldfarb-Shanno (BFGS) quasi-Newton method for solving optimization problems with stochastic objectives that arise in large scale machine learning…
RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is…
Following early work on Hessian-free methods for deep learning, we study a stochastic generalized Gauss-Newton method (SGN) for training DNNs. SGN is a second-order optimization method, with efficient iterations, that we demonstrate to…
We consider the development of practical stochastic quasi-Newton, and in particular Kronecker-factored block-diagonal BFGS and L-BFGS methods, for training deep neural networks (DNNs). In DNN training, the number of variables and components…
Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods,…
Quasi-Newton methods are ubiquitous in deterministic local search due to their efficiency and low computational cost. This class of methods uses the history of gradient evaluations to approximate second-order derivatives. However, only…
In Part I of this work, we have proposed a general framework of decentralized stochastic quasi-Newton methods, which converge linearly to the optimal solution under the assumption that the local Hessian inverse approximations have bounded…
Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational…
Optimization is important in machine learning problems, and quasi-Newton methods have a reputation as the most efficient numerical schemes for smooth unconstrained optimization. In this paper, we consider the explicit superlinear…
We extend the well-known BFGS quasi-Newton method and its memory-limited variant LBFGS to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: the…
Training in supervised deep learning is computationally demanding, and the convergence behavior is usually not fully understood. We introduce and study a second-order stochastic quasi-Gauss-Newton (SQGN) optimization method that combines…
Quasi-Newton methods still face significant challenges in training large-scale neural networks due to additional compute costs in the Hessian related computations and instability issues in stochastic training. A well-known method, L-BFGS…
Neural networks are trained by optimizing multi-dimensional sets of fitting parameters on non-convex loss landscapes. Low-loss regions of the landscapes correspond to the parameter sets that perform well on the training data. A key issue in…
Update formulas for the Hessian approximations in quasi-Newton methods such as BFGS can be derived as analytical solutions to certain nearest-matrix problems. In this article, we propose a similar idea for deriving new limited memory…
We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…
Physics-informed machine learning and inverse modeling require the solution of ill-conditioned non-convex optimization problems. First-order methods, such as SGD and ADAM, and quasi-Newton methods, such as BFGS and L-BFGS, have been applied…