We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing s…
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48 results for “proximal Newton-type method”
Develops a scalable framework for optimizing superposition-structured models.
problem Insufficient interpretability and generalization performance of simple structural models.
method Proximal Newton-type method with smoothed conic dual approach and LBFGS updating formula.
result Achieves super-linear convergence rate for optimizing superposition-structured models.
Unified Newton-type methods for convex optimization using generalized self-concordant functions.
problem Designing efficient Newton-type methods for convex optimization.
method Introducing generalized self-concordant functions and developing Newton-type methods.
result Unified framework for global and local convergence of Newton-type methods.
A new algorithm speeds up machine learning by solving large-scale problems more efficiently.
problem Efficiently solving large-scale machine learning problems with regularization.
method Subsampled proximal Newton-type method that leverages finite sum structure and recent stochastic first-order methods.
result The method achieves faster convergence than state-of-the-art methods for non-smooth regularizers.
New algorithms solve nonconvex-nonconcave minimax optimization problems.
problem Solving minimax optimization problems in machine learning.
method Two novel Newton-type algorithms for nonconvex-nonconcave minimax optimization.
result Proved local convergence at strict local minimax points.
Estimates MoE models with feature selection for high-dimensional data.
problem Estimation and feature selection in Mixtures-of-Experts models with high-dimensional predictors.
method Regularized maximum likelihood estimation with proximal-Newton EM algorithm.
result Good performance in recovering sparse solutions, parameter estimation, and clustering of heterogeneous data.
New method solves convex optimization faster than NAG.
problem Unconstrained smooth convex optimization problems.
method Accelerated quasi-Newton proximal extragradient (A-QPNE) method.
result Achieves a faster convergence rate of .
We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably \emph{improves} with the data size, requiring an essentially constant number of…
GIANT optimizes distributed computing by improving Newton method efficiency.
problem Efficiently solving empirical risk minimization problems in distributed environments.
method GIANT combines local ANT directions to form a GIANT direction, averaging communications and computations.
result GIANT achieves faster convergence compared to first-order and existing Newton-type methods.
Unified framework for two types of matrix Lie group preconditioners in SGD.
problem Improving optimization efficiency in machine learning models.
method Unified framework for Newton and Fisher type preconditioners on matrix Lie groups.
result Efficient estimation of preconditioners on matrix Lie groups.
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.
A new optimizer combines Newton and ADMM for faster classification.
problem Slower convergence of first-order methods in distributed learning.
method Integrates GPU-accelerated Newton solver with ADMM for multiclass classification.
result Significantly reduces the time to solution and generalization error.
The paper optimizes policies constrained to Schur stabilizing controllers using a Newton-type algorithm.
problem Optimizing policies under linear constraints in control systems.
method Newton-type algorithm on a manifold of Schur stabilizing controllers with a Riemannian metric.
result Local convergence guarantees for the Newton-type algorithm without relying on exponential mapping or retractions.
Empirical study shows second-order methods improve non-convex ML problems.
problem Slow convergence and hyper-parameter sensitivity in first-order methods.
method Sub-sampled trust region and adaptive regularization with cubics algorithms.
result Second-order methods are computationally competitive and robust to hyper-parameters.
FedNew: A Communication-Efficient and Privacy-Preserving Newton-Type Method for Federated Learningcs.LG
FedNew improves federated learning efficiency and privacy.
problem Low communication efficiency and privacy issues in Newton-type methods for federated learning.
method Introduces a two-level framework using ADMM for inverse Hessian-gradient approximation and Newton's method for global model updates, reducing communication overhead.
result FedNew achieves superior communication efficiency and privacy compared to existing methods.
New inexact proximal gradient methods solve non-convex optimization problems.
problem Solving non-convex optimization problems with non-smooth regularization.
method Proposed three inexact proximal gradient algorithms, including basic and Nesterov's accelerated versions.
result Theoretical analysis shows convergence rates similar to exact methods.
Improved sampling guarantees for weakly log-concave distributions.
problem Sampling from distributions that are not strongly log-concave.
method Proximal sampler with convergence guarantees under weaker assumptions.
result New state-of-the-art sampling guarantees for various target distributions.
Paper proposes FONE for efficient distributed estimation and inference.
problem Efficient distributed estimation and inference for non-differentiable convex losses.
method Proposes a multi-round distributed estimation procedure using a First-Order Newton-type Estimator (FONE).
result FONE efficiently estimates for non-differentiable losses, facilitating inference.
Improved robustness in optimization methods using second-order information.
problem Scalability and sensitivity to mini-batch size in optimization methods.
method Mini-Batch Stochastic Variance-Reduced Newton () algorithm incorporating partial second-order information.
result Achieves a fast linear convergence rate independent of mini-batch size for large data sizes.
Innovative method solves nonconvex optimization on manifolds.
problem Nonconvex optimization problems on Riemannian manifolds.
method Intrinsic Riemannian proximal gradient method.
result Converges for nonconvex or nonembedded problems.
Stochastic version of proximal distance algorithm analyzed and validated.
problem Optimization of constrained estimation problems.
method Stochastic proximal distance algorithm, with convergence guarantees and finite error bounds.
result Convergence guarantees and finite error bounds for the first time.
The paper connects a proximal method to stochastic filters and Bayes updates.
problem Large-scale optimization and probabilistic methods for regression.
method Explicit form of Bayes updates for linear regression and general sequential setting.
result The incremental proximal method can be realized by the Kalman filter for linear-quadratic cost functions.
Proximal splitting methods solve rank-constrained convex problems locally.
problem Solving optimization problems with rank constraints.
method Proximal splitting algorithms with conditions on rank constraint convex envelopes.
result Proximal splitting methods converge locally to solutions under convex relaxation conditions.
On parameter identification in stochastic differential equations by penalized maximum likelihoodstat.CO
In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed operator equation with a deterministic forward operator described by the Fokker-Pl…
Unified framework for training neural networks with non-smooth, non-convex regularizers.
problem Training neural networks with non-smooth, non-convex regularizers.
method ProxGen framework for stochastic proximal gradient descent.
result ProxGen framework achieves the same convergence rate as standard methods and outperforms subgradient-based approaches.
Proximal methods avoid local minima in weakly convex problems.
problem Weakly convex optimization problems with strict saddle properties.
method Proximal methods on nonsmooth functions with strict saddle guarantees.
result Proximal methods converge to local minimizers only, when initialized randomly.
Proposes a probabilistic optimization method for large-scale problems.
problem Large-scale regularized optimization problems.
method Develops a probabilistic interpretation of the incremental proximal gradient algorithm and uses Bayesian filtering.
result Makes it possible to solve large-scale problems using well-known Bayesian filters.
Unified analysis of EG and OGDA for saddle point problems using proximal point method.
problem Solving saddle point problems in bilinear and strongly convex-strongly concave settings.
method Unified analysis as approximations of the proximal point method.
result Unified analysis of EG and OGDA for saddle point problems.
A scalable framework preserves personalized higher-order network proximities.
problem Lack of expressive methods to preserve personalized higher-order network proximities.
method Incorporates random walk into a sound objective to preserve arbitrary higher-order proximities and introduces random walk with restart for personalized-weighted preservation.
result Consistently and substantially outperforms state-of-the-art methods on real-world networks.
Deep neural networks improve proximal inference for causal effects.
problem Estimating causal effects in the presence of unmeasured confounders.
method Flexible deep neural network to estimate the bridge function.
result Achieves state-of-the-art performance on benchmarks.
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole objective function is strongly convex. Such problems often arise in machine lea…
A new method tackles nonconvex optimization with penalties and proximal terms.
problem Nonconvex optimization problems with equality and inequality constraints.
method Inexact proximal augmented Lagrangian method (P-ALM) with adaptive penalty and proximal parameters.
result Effective convergence properties and numerical superiority over traditional methods.
A new method solves convex optimization problems on manifolds efficiently.
problem Optimization on Hadamard manifolds with convex objectives.
method Intrinsic Riemannian proximal gradient method.
result Sublinear and linear convergence rates for convex and strongly convex problems, respectively.
EPINE enhances network embedding by improving adjacency matrix-based high-order proximity.
problem Inaccurate and poorly designed calculation of high-order proximity in network embedding.
method EPINE redefines high-order proximity intuitively and proposes a scalable algorithm for accurate calculation.
result EPINE outperforms existing methods in network reconstruction, link prediction, and node classification.
A relaxed proximal gradient descent algorithm for convergent plug-and-play with proximal denoiserstat.ML
New PnP algorithm converges with relaxed proximal gradient descent.
problem Convergence issues in PnP methods with deep denoisers.
method Relaxed proximal gradient descent for PnP with weakly convex regularization.
result Proposed PnP-PGD converges for a wider range of regularization parameters.
Proximal boosting improves gradient boosting for non-differentiable losses.
problem Minimizing non-differentiable losses in prediction models.
method Proximal point algorithm applied to gradient boosting.
result Proximal boosting outperforms gradient boosting in convergence rate and accuracy.
Develops a new SPP algorithm with variance reduction for weakly convex optimization.
problem Weakly convex, composite optimization problems.
method Inexact semismooth Newton framework with variance reduction for stochastic proximal point updates.
result Establishes convergence results for the proposed algorithm.
Inertial proximal gradient algorithm shows monotonically decreasing values.
problem Optimizing functions with inertia.
method Proximal gradient algorithm with alternated inertia.
result Algorithm with alternated inertia achieves monotonically decreasing functional values.
Introduces PPMM algorithm for nonconvex robust regression problems.
problem Nonconvex tuning-free robust regression problems.
method PPMM algorithm with inner subproblems solved by SSN-PPA.
result Converges to d-stationary point with KL property.
Variance Reduction and Low Sample Complexity in Stochastic Optimization via Proximal Point Methodmath.OC
New method reduces variance in stochastic optimization with high confidence.
problem Achieving high-probability guarantees in stochastic optimization with weaker noise assumptions.
method Stochastic proximal point method combining proximal subproblem solver and probability booster.
result Demonstrates convergence with low sample complexity under bounded variance assumptions.
This paper converts ADMM to proximal gradient for efficient sparse estimation.
problem Sparse estimation problems like fused lasso and convex clustering.
method General method converting ADMM to proximal gradient, assuming Lipschitz continuity of derivative.
result Significant improvement in efficiency for sparse estimation problems.
CFR-Pro enhances treatment effect estimation by incorporating local proximity.
problem Treatment selection bias in HTE estimation from observational data.
method Proximity-enhanced CounterFactual Regression (CFR-Pro) with pair-wise proximity regularizer and subspace projector.
result Significantly outperforms competitors in HTE estimation accuracy.
New methods improve convergence rate of zeroth-order proximal stochastic algorithms.
problem Nonconvex nonsmooth optimization problems with infeasible gradients.
method ZO-ProxSVRG and ZO-ProxSAGA with variance reduction techniques.
result Convergence rate improved to from .
Adaptive methods improve gradient descent and proximal gradient for convex optimization.
problem Improving efficiency of gradient descent and proximal gradient methods.
method Adaptive versions of GD and ProxGD using local curvature information.
result Proved convergence with local Lipschitz gradient assumptions.
A New Inexact Proximal Linear Algorithm with Adaptive Stopping Criteria for Robust Phase Retrievalmath.OC
New algorithm solves phase retrieval with adaptive stopping criteria.
problem Robust phase retrieval problem as nonsmooth, nonconvex optimization.
method Inexact proximal linear algorithm with adaptive stopping criteria.
result Proposed methods are more efficient than existing methods.
FedDANE adapts DANE for federated learning, but underperforms compared to existing methods.
problem Federated learning's practical constraints and device heterogeneity.
method Adapted DANE for federated learning, providing convergence guarantees for convex and non-convex functions.
result Empirically, FedDANE underperforms compared to FedAvg and FedProx.
Stochastic proximal point algorithm with momentum converges faster and is more stable than standard methods.
problem Improving convergence and stability of stochastic optimization methods.
method Developed and analyzed the convergence and stability of the stochastic proximal point algorithm with momentum (SPPAM).
result SPPAM converges faster and is more stable than standard stochastic proximal point algorithm (SPPA) and stochastic gradient descent with momentum (SGDM).
Snake solves large graph optimization problems with fast proximal steps.
problem Optimization over large unstructured graphs with graph-specific regularization.
method Snake algorithm using random simple paths for proximal gradient steps.
result Convergence proven for the Snake algorithm.