Related papers: Variance-Reduced Stochastic Quasi-Newton Methods f…
The question of how to parallelize the stochastic gradient descent (SGD) method has received much attention in the literature. In this paper, we focus instead on batch methods that use a sizeable fraction of the training set at each…
Recent studies have illustrated that stochastic gradient Markov Chain Monte Carlo techniques have a strong potential in non-convex optimization, where local and global convergence guarantees can be shown under certain conditions. By…
In this paper, we explore the non-asymptotic global convergence rates of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method implemented with exact line search. Notably, due to Dixon's equivalence result, our findings are also applicable to…
We introduce some new proximal quasi-Newton methods for unconstrained multiobjective optimization problems (in short, UMOP), where each objective function is the sum of a twice continuously differentiable strongly convex function and a…
The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…
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…
This work studies the usage of well-known smoothed total variation regularization for solving an atmospheric tomography problem named as {\em GPS-tomography} in some quasi-Newton methods. That is we solve an unconstrained, convex, smooth…
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…
First-order methods like stochastic gradient descent(SGD) are recently the popular optimization method to train deep neural networks (DNNs), but second-order methods are scarcely used because of the overpriced computing cost in getting the…
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…
In this work, we propose FedSSO, a server-side second-order optimization method for federated learning (FL). In contrast to previous works in this direction, we employ a server-side approximation for the Quasi-Newton method without…
Data privacy and security becomes a major concern in building machine learning models from different data providers. Federated learning shows promise by leaving data at providers locally and exchanging encrypted information. This paper…
Despite the impressive numerical performance of the quasi-Newton and Anderson/nonlinear acceleration methods, their global convergence rates have remained elusive for over 50 years. This study addresses this long-standing issue by…
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…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…
We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive…
In compressed sensing (CS) MRI, model-based methods are pivotal to achieving accurate reconstruction. One of the main challenges in model-based methods is finding an effective prior to describe the statistical distribution of the target…
Quasi-Newton methods refer to a class of algorithms at the interface between first and second order methods. They aim to progress as substantially as second order methods per iteration, while maintaining the computational complexity of…
We present a distributed quasi-Newton (DQN) method, which enables a group of agents to compute an optimal solution of a separable multi-agent optimization problem locally using an approximation of the curvature of the aggregate objective…
Distributed computing is critically important for modern statistical analysis. Herein, we develop a distributed quasi-Newton (DQN) framework with excellent statistical, computation, and communication efficiency. In the DQN method, no…