arXiv research

Study shows non-symmetric convex sets have full boundary limits.

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…

Stochastic proximal point algorithm with momentum converges faster and is more stable than standard methods.

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…

Paper relates asymptotic dimension to cofinal dimension using coarse proximities.

Deep neural networks improve proximal inference for causal effects.

Improved sampling guarantees for weakly log-concave distributions.

Continuous MDS embeds sequences of dissimilarities in Euclidean space.

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…

The paper analyzes two ISGD modes for statistical inference, deriving error bounds and confidence intervals.

The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where the groups are a priori unknown. The OSCAR regularizer has a non-trivial proximit…

We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides a straightforward way of favouring prescribed sparsity patterns, such as orderin…

CFR-Pro enhances treatment effect estimation by incorporating local proximity.

This paper studies fixed sets in ribbon complexes using descriptive proximity spaces.

New PnP algorithm converges with relaxed proximal gradient descent.

Improves RL algorithms with two techniques.

A new method for RLHF using proximal point Nash learning.

Paper proposes a new method for supervised manifold learning using random forest proximities.

Improved shuffling gradient methods converge faster for nonsmooth convex optimization.

New study shows Gaussian samplers struggle with heavy-tailed targets, while stable samplers excel.

In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be realized with, Bayes updates. We give the explicit form of the updates for the linear regression problem and show that there is a one-to-one …

The paper analyzes PPM for nonconvex-nonconcave problems, identifying three regions with varying convergence guarantees.

Stochastic gradient descent (SGD) is one of the most widely used optimization methods for parallel and distributed processing of large datasets. One of the key limitations of distributed SGD is the need to regularly communicate the gradients between different computation nodes. To reduce this communication bottleneck, …

This paper accelerates TV regularization algorithms by unrolling proximal gradient descent.

New algorithm solves non-convex, non-differentiable min-max games.

RFX accelerates and compresses Random Forests for large datasets.

Enhances Bayesian model selection for high-dimensional problems.

Improved sampling algorithm with state-of-the-art complexity bounds.

This paper improves cross-domain learning using random forests for manifold alignment.

Complex embeddings handle non-metric proximity data better than traditional methods.

Enhances counterfactual explanations with more valid and informative saliency maps.

Proximal policy optimization(PPO) has been proposed as a first-order optimization method for reinforcement learning. We should notice that an exterior penalty method is used in it. Often, the minimizers of the exterior penalty functions approach feasibility only in the limits as the penalty parameter grows increasingly…

Unified framework for training neural networks with non-smooth, non-convex regularizers.

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…

I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framewor…

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…

Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be solved in polynomial time via a natural convex relaxation, known as Compressive …

Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, $ε$-graphs and $k$-NN graphs can lead to poor performance in the presence of proximal and unbalanced data. This is because spectral methods based…

ALP outperforms other data descriptors in one-class classification.

Policy-gradient method controls multiple non-cohesive targets.

We study the Proximal Langevin Algorithm (PLA) for sampling from a probability distribution $ν= e^{-f}$ on $\mathbb{R}^n$ under isoperimetry. We prove a convergence guarantee for PLA in Kullback-Leibler (KL) divergence when $ν$ satisfies log-Sobolev inequality (LSI) and $f$ has bounded second and third derivatives. Thi…

Extends GCNs to directed graphs for better performance.

Proximal Mediation Analysis with Hidden Recanting Witnesses

This article introduces planar shape signatures derived from homology nerves, which are intersecting 1-cycles in a collection of homology groups endowed with a proximal relator (set of nearness relations) that includes a descriptive proximity. A 1-cycle is a closed, connected path with a zero boundary in a simplicial c…

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…

Two new methods solve nonsmooth optimization on Riemannian Stiefel manifold.

Improves time series classification with forest proximities.

The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence rates are also limited to linear convergence. Due to the mathematical techniques, th…