arXiv research

Proposes a Quasi-Newton trust region method for policy optimization in reinforcement learning.

New quasi-Newton method guarantees global superlinear convergence.

Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newto…

A new quasi-Newton method uses cubic regularization to avoid saddle points in deep learning.

Improved training of large-scale neural networks with reduced variance noise.

New method uses adaptive sampling for optimization in uncertain conditions.

This paper improves NAQ method for faster convergence on Tensorflow.

In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties of this method, both in the exact and inexact setting, in the case when the obje…

Paper proposes a new method to efficiently incorporate curvature information in stochastic optimization.

Paper develops a robust PP distributed quasi-Newton estimation for Byzantine machines.

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 memory or data are collected in real-time). In our proposed framework, stochasticity…

New method improves zeroth-order stochastic optimization with adaptive sampling.

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 attractive algorithms. In essence, this is achieved by learning the second-order (…

Paper proposes a quasi-Newton method for nonlinear equations with global convergence guarantees.

New adaptive first-order methods improve on quasi-Newton variants.

Spark implementation for distributed function minimization.

Improved complexity for smooth nonconvex optimization using quasi-Newton methods.

Develops a new method for solving nonsmooth nonconvex optimization problems.

New method achieves superlinear convergence rate with limited memory.

SGD vs quasi-Newton optimization in neural networks: different landscapes, different generalizability.

Bayesian coresets improved with random sampling and quasi-Newton optimization.

Novel algorithm accelerates PnP methods for image deblurring and super-resolution.

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 learning (RL), are generally restricted to the class of first-order algorithms, lik…

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 estimates that have harmful effects on the robustness of the iteration. In this paper…

Apollo improves nonconvex stochastic optimization efficiency.

During recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second order information. In this work we propose a direct least-squares approach conceptually similar to…

Pathfinder uses quasi-Newton optimization for variational inference.

Paper proposes a faster federated learning method for logistic regression.

New method solves convex optimization faster than NAG.

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 involve fine-tuning many hyper-parameters. Quasi-Newton approaches based on the lim…

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 MLE for learning Conditional Random Fields (CRFs), which are a popular class of …

Develops efficient quasi-Newton methods for training deep neural networks.

This manuscript proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems $Bx = b$ with positive definite $B$ for $x$. The goal is to replace the point estimates returned by existing methods with a Gaussian posterior belief over the elements of the inverse of $B$, which can …

New method speeds up change-point detection in data sequences.

Novel approach simplifies VI problems with faster performance.

A new optimization method handles Euclidean bounds efficiently.

Incorporating second order curvature information in gradient based methods have shown to improve convergence drastically despite its computational intensity. In this paper, we propose a stochastic (online) quasi-Newton method with Nesterov's accelerated gradient in both its full and limited memory forms for solving lar…

Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Ne…

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). The key challenges of averaging, adding, and subtracting multipl…

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 is established. Lower and upper bounds on the Hessian eigenvalues of the sample …

New method solves optimization problems faster than existing methods.

Predictive coding networks are shown to be stable, robust, and converge faster than backpropagation.

A new distributed optimization method for ERM problems.

Pseudo-marginal Metropolis-Hastings (pmMH) is a versatile algorithm for sampling from target distributions which are not easy to evaluate point-wise. However, pmMH requires good proposal distributions to sample efficiently from the target, which can be problematic to construct in practice. This is especially a problem …

New methods use Kronecker-factored approximations for faster deep learning optimization.

Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to learn transforms from raw data attracts increasing attention. However, this adds…

Study evaluates three ML models for high-frequency trading.

A new optimization method improves deep learning accuracy without hyper-parameter tuning.