arXiv research

New algorithm solves phase retrieval with adaptive stopping criteria.

Paper analyzes convergence of proximal algorithm in metric spaces without geodesic convexity.

Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are several fundamental problems that remain open. First, existing methods fail to preser…

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

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 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…

In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiable function and a proper closed convex function. Under the error bound condition used in [19] for analyzing the convergence of the proximal gradient algorithm, we show that there exists a thresho…

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in …

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 propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth term and multiple stochastic nonsmooth terms. In each iteration, our splitting t…

The paper addresses nonconvex penalized LAD estimation in partial linear models using DNNs.

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 proposes an efficient algorithm for solving Schatten-$p$ quasi-norm problems.

Large models are prevalent in modern machine learning scenarios, including deep learning, recommender systems, etc., which can have millions or even billions of parameters. Parallel algorithms have become an essential solution technique to many large-scale machine learning jobs. In this paper, we propose a model parall…

New method finds linear relationships across multiple data blocks using proximal gradient descent with $\ell_1$ constraint.

New insights show NAG and FISTA converge linearly without knowing strong convexity modulus.

In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each proximal gradient step in APG so that a biconvex function $f(θ\mathbf{x})$ is minimi…

We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly non-differentiable but convex component. We propose a proximal stochastic gradie…

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…

Unified view connects CoCoA and ADMM for distributed ERM.

In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\sqrtκ)$ and thus achieves the optimal …

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and the non-smooth part is equipped with a simple proximal mapping. We propose a pr…

New model approximates sparse mean-CVaR portfolio optimization efficiently.

Paper proposes a new method for sparse spectral clustering on Stiefel manifold.

Paper introduces a new reinforcement learning method with improved performance.

Paper solves optimization problems with convex expectation constraints using a new algorithm.

Introduces PPMM algorithm for nonconvex robust regression problems.

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…

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…

Optimistic PPO variant solves linear MDPs with improved regret bound.

Modern proximal and stochastic gradient descent (SGD) methods are believed to efficiently minimize large composite objective functions, but such methods have two algorithmic challenges: (1) a lack of fast or justified stop conditions, and (2) sensitivity to the objective function's conditioning. In response to the firs…

Algorithm solves robust linear regression with block Lewis weights.

New algorithm accelerates single-pass SGD for generalized linear prediction.

A new algorithm solves signed Fréchet regression on manifolds with bounded curvature.

New algorithm solves minimax games with linear constraints.

A new optimization method, BPM, converges linearly in non-convex, non-smooth problems.

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…

A new method solves convex optimization problems on manifolds efficiently.

Proximal algorithms applied to current deformation into cycles.

Enhances KLR for indefinite kernels with $L_1$-norm regularization.

New PnP algorithm converges with relaxed proximal gradient descent.

The paper accelerates ISTA and FISTA algorithms for composite optimization problems.

Improved bounds for proximal gradient algorithms with computational errors.

We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic variance-reduced gradient descent algorithm (SVRG) and other randomized incremental opti…

Paper proposes iLPA for solving DC composite optimization problems, with applications to matrix completion with outliers.

We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression, across a wide range of problem settings. To achieve this, we establish a framewo…

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and proximal updates, respectively. The proposed algorithm is closely related to a p…

We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a conv…