Related papers: Symmetric Rank-One Quasi-Newton Methods for Deep L…
A novel regularization technique, AdaCubic, is proposed that adapts the weight of the cubic term. The heart of AdaCubic is an auxiliary optimization problem with cubic constraints that dynamically adjusts the weight of the cubic term in…
Quasi-Newton methods employ an update rule that gradually improves the Hessian approximation using the already available gradient evaluations. We propose higher-order secant updates which generalize this idea to higher-order derivatives,…
First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
We consider the class of optimization problems arising from computationally intensive L1-regularized M-estimators, where the function or gradient values are very expensive to compute. A particular instance of interest is the L1-regularized…
In this work, we develop first-order (Hessian-free) and zero-order (derivative-free) implementations of the Cubically regularized Newton method for solving general non-convex optimization problems. For that, we employ finite difference…
We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling…
In modern deep learning, highly subsampled stochastic approximation (SA) methods are preferred to sample average approximation (SAA) methods because of large data sets as well as generalization properties. Additionally, due to perceived…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
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…
In this work, we propose an optimization algorithm which we call norm-adapted gradient descent. This algorithm is similar to other gradient-based optimization algorithms like Adam or Adagrad in that it adapts the learning rate of stochastic…
We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are…
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…
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…
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…
Optimization in Deep Learning is mainly dominated by first-order methods which are built around the central concept of backpropagation. Second-order optimization methods, which take into account the second-order derivatives are far less…
First-order optimizers are reliable but slow in sharp, anisotropic regions. We study a curvature-adaptive method that periodically sketches a low-rank Hessian subspace via Hessian--vector products and preconditions gradients only in that…
Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…
Second-order methods have the capability of accelerating optimization by using much richer curvature information than first-order methods. However, most are impractical for deep learning, where the number of training parameters is huge. In…