A new method solves convex optimization on curved spaces.
problem Optimization on curved spaces with non-smooth functions.
method Convex bundle method on Riemannian manifolds.
result The method converges to a minimizer under mild conditions.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “proximal bundle method”
New method optimizes MAP inference for structured problems.
problem Structured energy minimization problems
method Proximal bundle method with block-coordinate Frank-Wolfe
result Empirically outperforms state-of-the-art algorithms
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 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.
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic sol…
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.
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.
The study constructs a Legendrian cycle for -sets and proves Reilly-type variational formulae.
problem Understanding higher-order mean curvature integrals of non-smooth sets.
method Construction of a Legendrian cycle and analysis of proximal unit normal bundles.
result Reilly-type variational formulae for higher-order mean curvature integrals of -sets.
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.
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…
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.
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.
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.
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.
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).
New method uses zeroth-order queries to approximate proximal sampling efficiently.
problem Approximating proximal sampling with zeroth-order information.
method Direct simulation of heat flow dynamics, treating intermediate distribution as Gaussian mixture.
result Inherits exponential convergence under isoperimetric conditions, avoids rejection sampling.
New method for efficient proximal mapping of 1-path-norm in shallow networks.
problem Efficiently handling the 1-path-norm of shallow neural networks.
method Closed-form proximal operator for efficient computation and upper bound on Lipschitz constant.
result Proximal mapping allows robust training against adversarial perturbations.
This work simplifies proximal mapping for low-rank norms.
problem Efficient computation of proximal mappings for low-rank inducing norms.
method Reduces proximal mapping to nested binary search, solving simpler problems analytically.
result Simplified computation of proximal mappings for various norms.
Optimizes convergence rate of stochastic proximal algorithms for composite convex problems.
problem Solving composite convex optimization problems with composite regularizers.
method Analyzed proximal stochastic gradient method and randomized incremental proximal method under relaxed variance assumptions.
result Proves convergence rate for last iterate of both algorithms under componentwise convexity and smoothness.
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.
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.
We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hen…
Proposes a new metric learning method for image recognition.
problem Improving image recognition performance using learned distance representations.
method Introduces a Generalized Hybrid Metric Loss (GHM-Loss) to learn hybrid proximity features combining geometric and probabilistic spaces.
result Demonstrates superior performance compared to existing methods on public datasets.
Paper proposes a new method for supervised manifold learning using random forest proximities.
problem Existing supervised manifold learning methods fail to uncover meaningful embeddings due to using class-conditional distances.
method Proposes a data-geometry-preserving variant of random forest proximities as an initialization for manifold learning methods.
result Local and global structure preservation is near universal across manifold learning approaches using diffusion-based algorithms.
Extends multidimensional scaling to analyze three-way asymmetric proximities.
problem Analyzing asymmetric and three-way proximities in a Euclidean space.
method Unified h-plot methodology for three-way asymmetric proximities, including symmetric and conditional frameworks.
result Identification of archetypal profiles and clustering structures.
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…
LPOM approximates neural nets with proximal operators for efficient training.
problem Training feed-forward neural networks efficiently and avoiding gradient issues.
method Rewriting activation functions as proximal operators, using block coordinate descent.
result LPOM converges and performs well on MNIST and CIFAR-10.
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.
Introduces a new divergence measure for optimal transport.
problem Optimal transport distances and information divergences.
method Infimal convolution formulation of proximal optimal transport divergence.
result Establishes connections to dynamic formulations and partial differential equations.
We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the qu…