Related papers: Coordinate Linear Variance Reduction for Generaliz…

We investigate the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through a cardinality constraint. While Branch-and-Bound (BnB) frameworks can certify optimality using perspective…

We study the reinforcement learning (RL) problem in a constrained Markov decision process (CMDP), where an agent explores the environment to maximize the expected cumulative reward while satisfying a single constraint on the expected total…

Generalized Disjunctive Programming (GDP) provides a powerful framework for combining algebraic constraints with logical disjunctions. To solve these problems, mixed-integer reformulations are required, but traditional reformulation…

This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as…

We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…

Large-scale linear programs (LPs) arise in many decision systems, including ranking, allocation, and matching problems that must be solved repeatedly at massive scale. Prior work such as ECLIPSE and LinkedIn's open-source DuaLip showed that…

Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…

In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…

Regularized estimators in the context of group variables have been applied successfully in model and feature selection in order to preserve interpretability. We formulate a Distributionally Robust Optimization (DRO) problem which recovers…

This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…

Generalized compressed sensing (GCS) is a paradigm in which a structured high-dimensional signal may be recovered from random, under-determined, and corrupted linear measurements. Generalized Lasso (GL) programs are effective for solving…

In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…

In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…

First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…

The goal in {\em reconfiguration problems} is to compute a {\em gradual transformation} between two feasible solutions of a problem such that all intermediate solutions are also feasible. In the {\em Matching Reconfiguration Problem} (MRP),…

We consider a multi-block separable convex optimization problem with the linear constraints, where the objective function is the sum of m individual convex functions without overlapping variables. The linearized version of the generalized…

The sparse linear reconstruction problem is a core problem in signal processing which aims to recover sparse solutions to linear systems. The original problem regularized by the total number of nonzero components (also known as $L_0$…

Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…

Graph sampling with noise is a fundamental problem in graph signal processing (GSP). Previous works assume an unbiased least square (LS) signal reconstruction scheme and select samples greedily via expensive extreme eigenvector computation.…

Recent works have shown that imposing tensor structures on the coefficient tensor in regression problems can lead to more reliable parameter estimation and lower sample complexity compared to vector-based methods. This work investigates a…