相关论文: Adaptive Step Sizes in Variance Reduction via Regu…

Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample…

We propose a trust-region method for finite-sum minimization with an adaptive sample size adjustment technique, which is practical in the sense that it leads to a globally convergent method that shows strong performance empirically without…

We consider convex optimization problems with a possibly nonsmooth objective function in the form of a mathematical expectation. The proposed framework (AN-SPS) employs Sample Average Approximations (SAA) to approximate the objective…

The paper introduces a new adaptive version of the Frank-Wolfe algorithm for relatively smooth convex functions. It is proposed to use the Bregman divergence other than half the square of the Euclidean norm in the formula for step-size.…

We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…

We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…

Variable metric proximal gradient methods with different metric selections have been widely used in composite optimization. Combining the Barzilai-Borwein (BB) method with a diagonal selection strategy for the metric, the diagonal BB…

Adaptive gradient methods such as RMSProp and Adam use exponential moving estimate of the squared gradient to compute adaptive step sizes, achieving better convergence than SGD in face of noisy objectives. However, Adam can have undesirable…

The choice of the stepsize in first-order convex optimization is typically based on the smoothness constant and plays a crucial role in the performance of algorithms. Recently, there has been a resurgent interest in introducing adaptive…

We study finite-sum non-convex optimization $\min_{x\in\mathbb{R}^d} F(x) \;=\; \frac{1}{n}\sum_{i=1}^n f_i(x)$ and analyze a variance-reduced cubic Newton method based on EMA-smoothed SARAH estimators for both gradient and Hessian…

Regularized empirical risk minimization (rERM) has become important in data-intensive fields such as genomics and advertising, with stochastic gradient methods typically used to solve the largest problems. However, ill-conditioned…

We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive…

Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local…

In this work, we solve a 49-year open problem, the general optimal step-size for ADMM-type algorithms. For a convex program: $\text{min.} \,\, f({x}) + g({z})$, $\text{s.t.}\, {A}{x} - {B}{z} = {c} $, given an arbitrary fixed-point…

Primal-dual algorithms for the resolution of convex-concave saddle point problems usually come with one or several step size parameters. Within the range where convergence is guaranteed, choosing well the step size can make the difference…

We propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily…

Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…

The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones.…

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…

In this paper, we investigate a class of non-convex sum-of-ratios programs relevant to decision-making in key areas such as product assortment and pricing, and facility location and cost planning. These optimization problems, characterized…