相关论文: A Dense Initialization for Limited-Memory Quasi-Ne…

In large-scale optimization, when either forming or storing Hessian matrices are prohibitively expensive, quasi-Newton methods are often used in lieu of Newton's method because they only require first-order information to approximate the…

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…

This paper deals with regularized Newton methods, a flexible class of unconstrained optimization algorithms that is competitive with line search and trust region methods and potentially combines attractive elements of both. The particular…

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…

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…

In this work, we consider methods for large-scale and nonconvex unconstrained optimization. We propose a new trust-region method whose subproblem is defined using a so-called "shape-changing" norm together with densely-initialized…

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…

We study the solution of symmetric positive-definite linear systems by way of families of full- and limited-memory methods. Our contributions are threefold. We first derive new relationships between the conjugate-gradient method (CG) and…

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…

We introduce the decentralized Broyden-Fletcher-Goldfarb-Shanno (D-BFGS) method as a variation of the BFGS quasi-Newton method for solving decentralized optimization problems. The D-BFGS method is of interest in problems that are not well…

For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional…

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…

This paper considers consensus optimization problems where each node of a network has access to a different summand of an aggregate cost function. Nodes try to minimize the aggregate cost function, while they exchange information only with…

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…

Deep neural networks achieve state-of-the-art performance for a range of classification and inference tasks. However, the use of stochastic gradient descent combined with the nonconvexity of the underlying optimization problems renders…

Reinforcement Learning (RL) algorithms allow artificial agents to improve their action selections so as to increase rewarding experiences in their environments. Deep Reinforcement Learning algorithms require solving a nonconvex and…

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…

We investigate quasi-Newton methods for minimizing a strictly convex quadratic function which is subject to errors in the evaluation of the gradients. The methods all give identical behavior in exact arithmetic, generating minimizers of…

We introduce a proximal limited--memory quasi--Newton scheme for minimizing the sum of a continuously differentiable function and a proper, lower semicontinuous and prox-bounded, possibly nonsmooth, function. Both functions might be…

Factorized layers--operations parameterized by products of two or more matrices--occur in a variety of deep learning contexts, including compressed model training, certain types of knowledge distillation, and multi-head self-attention…