Proposes a Quasi-Newton trust region method for policy optimization in reinforcement learning.
problem Lack of stepsize selection criterion and slow convergence in gradient descent for policy optimization.
method Uses a trust region method with Quasi-Newton approximation for the Hessian.
result Demonstrates improved performance and efficiency in continuous control tasks.
New quasi-Newton method guarantees global superlinear convergence.
problem Global convergence and superlinear convergence of quasi-Newton methods.
method Hybrid proximal extragradient method with online learning for Hessian approximation.
result First globally convergent quasi-Newton method with explicit superlinear convergence rate.
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…
This paper improves NAQ method for faster convergence on Tensorflow.
problem Non-convex optimization problems.
method Modified Nesterov's Accelerated Quasi-Newton (NAQ) method on Tensorflow.
result mNAQ converges better and faster than first and second order optimizers.
Stochastic quasi-Newton tackles noisy gradients in optimization.
problem Optimizing with noisy data in stochastic settings.
method Extends quasi-Newton methods to handle stochastic gradients through flexible Hessian modeling and line-search regularization.
result Demonstrates superior performance in maximum likelihood estimation for complex models.
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…
A new algorithm reduces variance in Riemannian stochastic quasi-Newton methods.
problem Minimizing the average of many loss functions on Riemannian manifolds.
method R-SQN-VR algorithm with variance reduction for non-convex and retraction-convex functions.
result The algorithm outperforms existing methods on manifold computations.
Paper develops a robust PP distributed quasi-Newton estimation for Byzantine machines.
problem Byzantine machines in distributed computing under Privacy Protection constraints.
method Robust PP distributed quasi-Newton estimation method that transmits only five vectors.
result Reduces privacy budgeting and transmission cost compared to gradient descent and Newton iteration.
Improved training of large-scale neural networks with reduced variance noise.
problem Training large-scale neural networks with high variance noise.
method Stochastic variance reduced Nesterov's Accelerated Quasi-Newton method (SVR-NAQ).
result Improved performance compared to conventional methods on benchmark problems.
Quasi-Newton methods improve deep learning optimization.
problem Solving non-convex optimization problems in deep learning.
method Constructing approximate Hessian matrices using quasi-Newton methods.
result Quasi-Newton methods achieve superlinear convergence.
Proposes a new stochastic quasi-Newton method with Nesterov's acceleration.
problem Improving convergence in large-scale non-convex optimization problems.
method Stochastic quasi-Newton method with Nesterov's accelerated gradient.
result Improved performance compared to classical and popular methods.
Novel algorithm accelerates PnP methods for image deblurring and super-resolution.
problem Efficiently solving inverse problems and imaging with provable convergence guarantees.
method Incorporates quasi-Newton steps into provable PnP framework based on proximal denoisers.
result 2--8x faster convergence compared to other provable PnP methods with similar quality.
A new quasi-Newton method tackles NMF with transform learning on orthogonal manifolds.
problem Efficiently learning transforms for NMF in non-convex optimization on orthogonal manifolds.
method Derives a quasi-Newton method on the orthogonal matrix manifold using sparse approximations of the Hessian.
result Outperforms state-of-the-art methods by orders of magnitude in experiments on synthetic and real audio data.
New probabilistic Newton-type algorithms for noisy optimization problems.
problem Noisy observations of cost functions and derivatives in nonlinear system identification.
method Probabilistic Gaussian process models and recent probabilistic line search routines.
result Probabilistic quasi-Newton approach delivers promising results on challenging problems.
Improved sampling for complex distributions using quasi-Newton proposals.
problem Sampling from complex, high-dimensional target distributions efficiently.
method Extended pseudo-marginal Metropolis-Hastings with quasi-Newton proposals.
result Quasi-Newton proposals outperform standard random-walk and Hessian-based proposals.
Bayesian coresets improved with random sampling and quasi-Newton optimization.
problem Efficiently approximate Bayesian posterior distributions for computationally expensive inference.
method Randomly select a subset of data points, then optimize weights using quasi-Newton method.
result First algorithm with high-probability KL divergence bound on coreset quality.
New method improves zeroth-order stochastic optimization with adaptive sampling.
problem Optimization problems without gradient information.
method Adaptive sampling quasi-Newton method using finite differences.
result Significant improvement in performance with adaptive sample sizes.
New trust-region algorithms improve ML performance with indefinite Hessians.
problem Training machine learning models with indefinite Hessians.
method Quasi-Newton trust-region framework for indefinite Hessians.
result Proposed methods outperform traditional BFGS and Hessian-free methods.
Efficient distributed algorithm for ERM with nonsmooth regularizers.
problem Solving Empirical Risk Minimization problems with nonsmooth regularization in a distributed setting.
method A distributed quasi-Newton algorithm using successive quadratic approximations and efficient subproblem solving.
result Global linear convergence for a broad range of non-strongly convex problems, reducing communication complexity.
A new method improves convergence in large-scale stochastic optimisation.
problem Improving convergence in large-scale stochastic optimisation problems.
method A direct least-squares approach with a Cholesky factor and adaptive line search.
result Improved convergence compared to existing methods on real-world problems.
New method improves Pham's algorithm for joint diagonalization.
problem Optimizing joint diagonalization of matrices for statistical learning.
method Quasi-Newton method for Pham's diagonalization criterion.
result Proposed method outperforms Pham's algorithm in experiments.
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 …
SGD vs quasi-Newton optimization in neural networks: different landscapes, different generalizability.
problem Understanding neural network optimization and generalizability.
method Comparison of stochastic gradient descent (SGD) and quasi-Newton optimization methods using computational tools.
result SGD solutions are separated by lower barriers than quasi-Newton solutions, but quasi-Newton solutions are deeper and more isolated.
Develops a new method for solving nonsmooth nonconvex optimization problems.
problem Solving nonsmooth nonconvex composite optimization problems with noisy gradient information.
method Combines stochastic higher order steps and additional stochastic proximal gradient steps.
result Global convergence to stationary points in expectation with favorable performance on large-scale problems.
Stochastic Newton and quasi-Newton methods solve large linear least-squares problems efficiently.
problem Efficiently solve large linear least-squares problems with limited computational resources.
method Introduce stochasticity in Newton and quasi-Newton approaches to handle large datasets.
result Stochastic Newton iterates may not converge to the least-squares solution.
Paper proposes a quasi-Newton method for nonlinear equations with global convergence guarantees.
problem Solving smooth and monotone nonlinear equations efficiently and globally.
method Hybrid proximal extragradient framework combined with online learning for Jacobian approximation.
result First global convergence results showing quasi-Newton method's advantage over extragradient method.
Improved complexity for smooth nonconvex optimization using quasi-Newton methods.
problem Finding ε-first-order stationary points of smooth functions with gradient information only.
method Two-level online learning approach involving quasi-Newton methods.
result Gradient complexity improved to O(d^(1/4)ε^(-13/8)) for d = O(ε^(-1/2)).
A new optimization method handles Euclidean bounds efficiently.
problem Optimization problems with Euclidean bounds.
method Riemannian limited-memory BFGS method combining quasi-Newton and Riemannian adaptations.
result Outperforms existing methods by several orders of magnitude.
A new quasi-Newton method uses cubic regularization to avoid saddle points in deep learning.
problem Avoiding saddle points and poor local minima in deep learning models.
method Limited-memory symmetric rank-one quasi-Newton approach with adaptive regularized cubics.
result The method effectively avoids saddle points and converges to better local minima.
Improved L-BFGS for large-scale ML with progressive batching.
problem Combining fast generalization with reliable line search in large-scale ML.
method Progressive batching, stochastic line search, stable quasi-Newton updating.
result Performs well on training logistic regression and deep neural networks.
New method uses adaptive sampling for optimization in uncertain conditions.
problem Optimizing functions with unknown gradients in uncertain environments.
method Adaptive sampling quasi-Newton method with finite differences and norm tests.
result Potential performance benefits of the proposed method demonstrated in preliminary experiments.
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 …
Apollo improves nonconvex stochastic optimization efficiency.
problem Nonconvex stochastic optimization challenges.
method Adaptive parameter-wise diagonal quasi-Newton method approximating Hessian.
result Significant improvements in convergence speed and generalization over SGD and Adam.
Paper proposes a faster federated learning method for logistic regression.
problem Federated learning for logistic regression with disjoint feature sets.
method Quasi-Newton method under additively homomorphic encryption.
result Significant reduction in communication rounds with minimal additional cost.
A new optimization method improves deep RL performance.
problem Optimizing deep RL algorithms to avoid saddle points and improve convergence.
method Limited-memory BFGS quasi-Newton method using line search strategy.
result Improved convergence and generalization characteristics with fast training time.
Paper proposes a new method to efficiently incorporate curvature information in stochastic optimization.
problem Minimizing nonconvex functions with limited curvature information.
method Structured stochastic quasi-Newton method using partial Hessian information.
result Global convergence to stationary point and local superlinear convergence rate established.
Study evaluates three ML models for high-frequency trading.
problem Improving accuracy and reliability of high-frequency trading strategies.
method Compared three models: cross-entropy loss + quasi-Newton, FCNN, and vector machine.
result Combination of cross-entropy loss and quasi-Newton outperformed other models.
A new method speeds up factor analysis for high-dimensional data.
problem Estimating covariance parameters in high-dimensional Gaussian data with limited observations.
method Matrix-free likelihood method using implicitly restarted Lanczos and limited-memory quasi-Newton algorithms.
result Our method is faster than EM without sacrificing accuracy.
Pathfinder uses quasi-Newton optimization for variational inference.
problem Approximating complex posterior distributions efficiently.
method Pathfinder combines quasi-Newton optimization with variational methods to approximate log densities.
result Pathfinder produces draws with lower KL divergence than ADVI and comparable to HMC, requiring fewer evaluations.
Proposes an accelerated optimization algorithm for composite objectives.
problem Gradient-based optimization with sparse solutions and high dimensions.
method Inexact variable-metric proximal point algorithm (QNing) with limited-memory BFGS.
result Significant improvements over competing methods in training machine learning models.
A new distributed optimization method for ERM problems.
problem Efficiently solving ERM problems with nonsmooth regularization in a distributed setting.
method Second-order distributed optimization using successive quadratic approximations and Hessian approximation.
result Global linear convergence for a broad range of non-strongly convex problems.
Two new sampling methods improve machine learning optimization.
problem Efficiently solving machine learning empirical risk minimization problems.
method Randomly sampled quasi-Newton methods for optimization.
result Sampled methods outperform classical variants in machine learning tasks.
A scalable distributed S-LSR1 algorithm reduces communication costs.
problem Efficiently scaling S-LSR1 for large-scale distributed optimization.
method Proposes DS-LSR1, a communication-efficient variant of S-LSR1.
result DS-LSR1 scales well in problem dimension and data points.
Paper investigates optimization methods for ICA on real signals, overcoming convergence issues.
problem Optimizing likelihood for ICA on real signals, especially with constrained white signals.
method Rewrites algorithms as quasi-Newton methods, focusing on Hessian approximation.
result Preconditioned ICA for Real Data (Picard) algorithm improves convergence on real signals.
Predictive coding networks are shown to be stable, robust, and converge faster than backpropagation.
problem Stability, robustness, and convergence of predictive coding networks.
method Dynamical systems theory and Lyapunov stability analysis.
result Predictive coding networks are Lyapunov stable and converge faster than backpropagation.
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…
Recurrent Neural Networks (RNNs) are powerful models that achieve exceptional performance on several pattern recognition problems. However, the training of RNNs is a computationally difficult task owing to the well-known "vanishing/exploding" gradient problem. Algorithms proposed for training RNNs either exploit no (or…
New adaptive first-order methods improve on quasi-Newton variants.
problem Designing efficient gradient methods for practical applications.
method Online scaled gradient methods (OSGM) with new adaptive methods OSGM-Best.
result OSGM-Best matches quasi-Newton variants but requires less memory and cheaper iterations.