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).
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.
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.
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.
In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a unified analysis as approximations of the classical proximal point method for solving…
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.
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.
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.
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.
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.
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.
Gradient boosting is a prediction method that iteratively combines weak learners to produce a complex and accurate model. From an optimization point of view, the learning procedure of gradient boosting mimics a gradient descent on a functional variable. This paper proposes to build upon the proximal point algorithm, wh…
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.
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.
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…
Improved random forest proximities capture data geometry.
problem Inaccurate random forest proximities do not reflect learned data geometry.
method Introduce RF-GAP: Geometry- and Accuracy-Preserving proximities.
result RF-GAP improves geometric representation in tasks like data imputation.
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…
We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling approaches we propose are appropriately accurate, the methods enjoy stronger conv…
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.
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.
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.
This paper studies fixed sets in ribbon complexes using descriptive proximity spaces.
problem Understanding fixed sets in ribbon complexes within descriptive proximity spaces.
method Introduces descriptive fixed sets and their properties in ribbon complexes, using descriptive proximally continuous maps.
result Establishes that proximal descriptive conjugacy preserves fixed sets in ribbon complexes.
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold M. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the distance function to a closed subset C of M; 2) solvability and implicit func…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is an iterative scheme born from the adaptation of proximal point algorithm to nois…
We consider saddle point problems which objective functions are the average of n strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence guarantees. However, these methods have a slow convergence when the condition n…
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.
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.
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…
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.
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.
Nonconvex and nonsmooth problems have recently attracted considerable attention in machine learning. However, developing efficient methods for the nonconvex and nonsmooth optimization problems with certain performance guarantee remains a challenge. Proximal coordinate descent (PCD) has been widely used for solving opti…
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.
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.
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.
The paper analyzes two ISGD modes for statistical inference, deriving error bounds and confidence intervals.
problem Statistical inference with implicit SGD for smooth convex functions.
method Proximal Robbins-Monro (proxRM) and proximal Polyak-Ruppert (proxPR) procedures for ISGD.
result Derives non-asymptotic error bounds and confidence interval estimators for model parameters.
This paper studies the lower bound complexity for the optimization problem whose objective function is the average of n individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for each individual component. For the strongly-convex case, we prove such an algorith…
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.
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.
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, regu…
We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this kind of problems can be classified into three classes. Algorithms in the first class rely on information of the subgradients of the objec…
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.
We introduce a binary embedding framework, called Proximity Preserving Code (PPC), which learns similarity and dissimilarity between data points to create a compact and affinity-preserving binary code. This code can be used to apply fast and memory-efficient approximation to nearest-neighbor searches. Our framework is …
Paper extends Brouwer Fixed Point Theorem with amiable and almost amiable fixed sets.
problem Extending the Brouwer Fixed Point Theorem to approximate fixed sets.
method Introducing shape boundary regions in CW spaces as amiable and almost amiable fixed subsets of dpc maps.
result Variation of Jordan Curve Theorem and Fixed Cell Complex Theorem.
Enhances local explainability and trust scores using RF proximities.
problem Improving local explainability and trust in random forest models.
method Rewriting RF predictions as weighted sums of training targets using proximities.
result Proximities provide a novel method to assess model predictions' correctness.
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including con…