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.
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).
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.
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.
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 methods for solving convex optimization problems with improved accuracy and convergence.
problem Solving stochastic convex optimization problems with improved accuracy and robustness.
method Approximate-proximal point (aProx) family, including stochastic subgradient, proximal point, and bundle methods.
result Improved models converge with probability 1 and enjoy optimal asymptotic normality results under weak assumptions.
New algorithm speeds up solving saddle-point problems with large condition numbers.
problem Solving saddle-point problems with large condition numbers.
method Proposes a stochastic proximal point algorithm that accelerates variance reduction methods.
result Reduces logarithmic term of condition number for iteration complexity.
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.
APO optimizes neural network parameters by amortizing proximal point methods.
problem Optimizing neural network parameters online and adaptively.
method APO framework that meta-learns proximal point parameters.
result APO can recover and outperform existing optimizers and schedules.
A new optimization method, BPM, converges linearly in non-convex, non-smooth problems.
problem Non-smooth and non-convex optimization challenges.
method Ball-Proximal Point Method (BPM), inspired by Proximal Point Method (PPM).
result BPM converges linearly and in a finite number of steps in non-convex, non-smooth problems.
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.
PDNS tackles multimodal sampling challenges using proximal point method.
problem Multimodal distributions with significant barriers between modes.
method Proximal point method on path measures, decomposing into simpler subproblems.
result PDNS effectively promotes thorough exploration across modes.
Proposes a new method for localized uncertainty quantification in random forests using proximity measures.
problem Localized uncertainty quantification in random forests for improved reliability of predictions.
method Forming localized distributions of Out-Of-Bag (OOB) errors around nearby points defined by similarity measures (proximities) to create prediction intervals for regression and trust scores for classification.
result Localized prediction intervals and trust scores enhance model accuracy and provide higher accuracy-rejection AUC scores than competing methods.
The paper tackles finding stationary points in stochastic convex optimization problems.
problem Finding stationary points for stochastic convex optimization problems.
method The approach relies on dimension theory to decompose the graph of the subdifferential of a convex function, showing how stochastic sampling preserves 'pieces' of these graphs, and allowing effective application of proximal-point-like methods.
result The paper provides convergence guarantees for finding stationary points in stochastic convex optimization problems.
A method for estimating the median of gradients in stochastic optimization.
problem Robust gradient estimation in stochastic optimization for various applications.
method Stochastic Proximal Point Method for median gradient estimation.
result The proposed method can converge even under heavy-tailed, state-dependent noise.
New algorithm improves convergence rates for convex optimization problems.
problem Convex optimization problems with noisy stochastic data.
method Stochastic proximal point algorithm with weak linear regularity condition.
result Achieves $\mathcal{O}\left(\frac{1}{k}
ight)$ convergence rate for SPP.
Improves time series classification with forest proximities.
problem Time series classification accuracy and efficiency.
method PF-GAP, an extension of RF-GAP proximities to proximity forests, combined with Multi-Dimensional Scaling and Local Outlier Factors.
result Forest proximities show stronger connection between misclassified points and outliers.
A new method for RLHF using proximal point Nash learning.
problem Capturing real human preferences in RLHF.
method Proximal point Nash learning, embedding self-play updates into a proximal point framework.
result High-probability last-iterate convergence for the combined method.
Develops a new algorithm for computing exact Wasserstein distance efficiently.
problem High computational complexity of exact Wasserstein distance computation.
method Inexact Proximal Point Method (IPOT) with approximate projections to the probability simplex.
result Algorithm converges to exact Wasserstein distance with theoretical guarantees and robust regularization parameter selection.
New method solves saddle-point problems faster than existing methods.
problem Large-scale saddle-point problems in optimization.
method Sequential subspace optimization with proximal regularization.
result Significantly better convergence compared to first-order methods.
Decentralized method solves saddle point problems with theoretical guarantees.
problem Solving saddle point problems in a decentralized network.
method Proximal point method adapted for decentralized networks.
result Converges to approximate stationarity with rate of O(1/√T).
A new method solves optimization problems over Stiefel manifold.
problem Optimization problems over the Stiefel manifold with smooth and nonsmooth components.
method Proximal gradient method based on retraction.
result The method globally converges to a stationary point and has iteration complexity.
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.
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…
New findings show Bregman proximal algorithms can get stuck near non-stationary points.
problem Bregman proximal algorithms can get stuck near non-stationary points, misleadingly suggesting convergence.
method Analysis of Bregman proximal algorithms and their behavior near non-stationary points.
result Bregman proximal algorithms can get stuck near spurious stationary points, even in convex problems.
We propose a new proximal, path-following framework for a class of constrained convex problems. We consider settings where the nonlinear---and possibly non-smooth---objective part is endowed with a proximity operator, and the constraint set is equipped with a self-concordant barrier. Our approach relies on the followin…
New analysis shows convergence rate of 1/k for gradient and extra-gradient methods.
problem Finding saddle points in convex-concave problems.
method Interpreted as proximal point method approximations, showing iterates remain bounded.
result Primal dual gap converges at rate O(1/k).
Riemannian Proximal Sampler improves sampling on manifold data.
problem Sampling from densities on Riemannian manifolds.
method Uses MBI and RHK oracles for high-accuracy sampling.
result Sampling with ε-accuracy requires O(log(1/ε)) iterations in KL divergence.
The paper analyzes convergence properties of NGA and PAMe for L1-norm PCA.
problem Finite-step convergence of L1-norm PCA algorithms. method Conditional subgradient and alternating maximization interpretations of NGA, and PAMe with extrapolation.
result Iterative points of modified NGA and PAMe remain constant after finitely many steps under certain conditions.
Two new algorithms improve federated optimization under second-order similarity.
problem Federated learning under communication constraints and second-order similarity.
method SVRP and Catalyzed SVRP algorithms combining proximal point evaluations, client sampling, and variance reduction.
result Achieves superior performance and uniformly improves upon existing algorithms for federated optimization under second-order similarity and strong convexity.
A new method reformulates Optimal Transport Conditional Flow Matching using proximal operators.
problem Optimal Transport Conditional Flow Matching (OT-CFM) for generating models.
method Reformulate OT-CFM using proximal operators and extended Brenier potential.
result OT-CFM dynamics are terminally normally hyperbolic for manifold-supported targets.
New algorithms accelerate model-based optimization for stochastic problems.
problem Optimizing model-based stochastic optimization problems efficiently.
method Proposed new model-based algorithms with acceleration and minibatch techniques.
result Non-asymptotic convergence guarantees with linear speedup in minibatch size.
Paper develops accelerated APCD for nonconvex nonsmooth problems with performance guarantees.
problem Efficient methods for nonconvex nonsmooth optimization problems with performance guarantees.
method Asynchronous Accelerated Proximal Coordinate Descent (AAPCD) for nonsmooth and nonconvex problems.
result AAPCD ensures that every limit point is a critical point and achieves linear and sublinear convergence rates.
Paper introduces a new reinforcement learning method with improved performance.
problem Designing and analyzing efficient reinforcement learning algorithms.
method Proximal gradient temporal difference learning (GTD) with accelerated algorithm GTD2-MP.
result GTD algorithms have linear complexity and improved convergence rate.
Two strategies for embedding new data points from proximity data are explored.
problem Embedding new data points using proximity data.
method Two competing strategies: projection and restricted reconstruction.
result Projection and restricted reconstruction can be derived from kernel methods.
New algorithms tackle machine learning problems using manifold proximal point methods.
problem Maximizing the ℓ1 norm of a linear map over the sphere in machine learning.
method Manifold Proximal Point Algorithms (ManPPA) and Stochastic ManPPA (StManPPA).
result ManPPA and StManPPA achieve faster convergence rates than existing methods.
Improves RL algorithms with two techniques.
problem Enhance off-policy RL performance.
method Formulates RL as proximal point iteration; uses value functions for improved action value estimate.
result Significant performance improvement on RL benchmarks.
New model approximates sparse mean-CVaR portfolio optimization efficiently.
problem NP-hard ℓ0-constrained mean-CVaR optimization. method Proximal alternating linearized minimization algorithm with nested fixed-point proximity.
result The model offers a guaranteed approximation of the ℓ0-constrained mean-CVaR model. Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with a tractable proximity operator and that the convex constraint set affords a self…
We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and solves…
Method uses NMF for clustering with partial distance measurements.
problem Proximity clustering with partial distance measurements.
method Nyström approximation with Nonnegative Matrix Factorization.
result Find nearly optimal clustering quality on synthetic and real-world data.
A new method combines extrapolation and line search for solving nonconvex, nonsmooth optimization problems.
problem Nonconvex, nonsmooth optimization problems in machine learning and image processing.
method Proximal gradient method with extrapolation and line search (PGels).
result The method reduces to existing algorithms under proper parameter choices and converges to stationary points.
The paper analyzes PPM for nonconvex-nonconcave problems, identifying three regions with varying convergence guarantees.
problem Challenges in nonconvex-nonconcave minimax optimization.
method Classic proximal point method with insights from the Moreau envelope.
result Identification of three regions with varying convergence guarantees for PPM.
PPOS improves PPO by smoothing the surrogate objective function.
problem Performance instability and optimization inefficiency in PPO.
method Use of a functional clipping method instead of a flat clipping method.
result PPOS conducts more accurate updates and outperforms other PPO variants.
Enhances supervised visualization for unseen data using autoencoders and random forest.
problem Lack of generalization to unseen test sets in supervised dimensionality reduction.
method Combines autoencoder and random forest proximities for out-of-sample extension.
result 40% reduction in training time with 10% of training data, achieving consistent quality.
A new method solves complex optimization problems with nonconvex and nonsmooth components.
problem Nonconvex nonsmooth optimization problems with coupled functions.
method Successive difference-of-convex approximation method using Moreau envelopes.
result The method generates bounded sequences with stationary points as accumulation points.
Two new methods solve nonsmooth optimization on Riemannian Stiefel manifold.
problem Optimization over nonsmooth, non-differentiable functions on Riemannian manifolds.
method R-ProxSGD and R-ProxSPB, generalizing proximal SGD and SpiderBoost.
result R-ProxSPB finds ε-stationary points with IFO complexity of Ø(ε^(-3)) in online and Ø(n + √nε^(-2)) in finite-sum cases.
Efficient algorithm solves sparse nonconvex regression problems.
problem Sparse nonconvex square-root-loss regression problems.
method Proximal majorization-minimization (PMM) algorithm with sparse semismooth Newton method.
result Converges to a d-stationary point with Kurdyka-Łojasiewicz property.