Related papers: Approximating Higher-Order Derivative Tensors Usin…
Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other…
Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely…
In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…
Quasi-Newton methods form an important class of methods for solving nonlinear optimization problems. In such methods, first order information is used to approximate the second derivative. The aim is to mimic the fast convergence that can be…
The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature…
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…
We propose a novel algorithm, termed soft quasi-Newton (soft QN), for optimization in the presence of bounded noise. Traditional quasi-Newton algorithms are vulnerable to such perturbations. To develop a more robust quasi-Newton method, we…
Optimization problems, arise in many practical applications, from the view points of both theory and numerical methods. Especially, significant improvement in deep learning training came from the Quasi-Newton methods. Quasi-Newton search…
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 methods for variational inequalities require precise…
An inexact framework for high-order adaptive regularization methods is presented, in which approximations may be used for the $p$th-order tensor, based on lower-order derivatives. Between each recalculation of the $p$th-order derivative…
We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic…
We propose an extension of quasi-Newton methods, and investigate the convergence and the robustness properties of the proposed update formulae for the approximate Hessian matrix. Fletcher has studied a variational problem which derives the…
We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…
This paper concerns exact linesearch quasi-Newton methods for minimizing a quadratic function whose Hessian is positive definite. We show that by interpreting the method of conjugate gradients as a particular exact linesearch quasi-Newton…
Gradient-based algorithms are one of the methods of choice for the optimisation of Markov Decision Processes. In this article we will present a novel approximate Newton algorithm for the optimisation of such models. The algorithm has…
Quasi-Newton algorithms are among the most popular iterative methods for solving unconstrained minimization problems, largely due to their favorable superlinear convergence property. However, existing results for these algorithms are…
Quasi-Newton (QN) methods provide an efficient alternative to second-order methods for minimizing smooth unconstrained problems. While QN methods generally compose a Hessian estimate based on one secant interpolation per iteration,…
This paper presents a model-free approximation for the Hessian of the performance of deterministic policies to use in the context of Reinforcement Learning based on Quasi-Newton steps in the policy parameters. We show that the approximate…
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…
In this paper, we consider stochastic second-order methods for minimizing a finite summation of nonconvex functions. One important key is to find an ingenious but cheap scheme to incorporate local curvature information. Since the true…