Related papers: Efficient Low-Rank Semidefinite Programming with R…

Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…

Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to…

Constrained discrete optimization problems are encountered in many areas of communication and machine learning. We consider the case where the objective function satisfies Bellman's optimality principle without the constraints on which we…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…

Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without…

This paper proposes a dual Riemannian alternating direction method of multipliers (ADMM) for solving low-rank semidefinite programs with unit diagonal constraints. We recast the ADMM subproblem as a Riemannian optimization problem over the…

Traditional dictionary learning methods are based on quadratic convex loss function and thus are sensitive to outliers. In this paper, we propose a generic framework for robust dictionary learning based on concave losses. We provide results…

Sample inefficiency is a long-lasting challenge in deep reinforcement learning (DRL). Despite dramatic improvements have been made, the problem is far from being solved and is especially challenging in environments with sparse or delayed…

Ordinal regression is a specialized supervised problem where the labels show an inherent order. The order distinguishes it from normal multi-class problem. Support Vector Ordinal Regression, as an outstanding ordinal regression model, is…

Alternating Direction Method of Multipliers (ADMM) is a popular method for solving large-scale Machine Learning problems. Stochastic ADMM was proposed to reduce the per iteration computational complexity, which is more suitable for big data…

Convex relaxations have emerged as a promising approach for verifying desirable properties of neural networks like robustness to adversarial perturbations. Widely used Linear Programming (LP) relaxations only work well when networks are…

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

Iterative algorithms are ubiquitous in the field of data mining. Widely known examples of such algorithms are the least mean square algorithm, backpropagation algorithm of neural networks. Our contribution in this paper is an improvement…

A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…

We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…

Sensitivity-based distributed programming (SBDP) is a decomposition method for solving large-scale nonlinear programs over graph-structured networks. However, its convergence depends on the strength and structure of subsystem coupling. To…

The classical hinge-loss support vector machines (SVMs) model is sensitive to outlier observations due to the unboundedness of its loss function. To circumvent this issue, recent studies have focused on non-convex loss functions, such as…