Related papers: Active-set Methods for Submodular Minimization Pro…

Sparsity promoting functions (SPFs) are commonly used in optimization problems to find solutions which are assumed or desired to be sparse in some basis. For example, the l1-regularized variation model and the Rudin-Osher-Fatemi total…

We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…

Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a…

The problem of sensor network localization (SNL) can be formulated as a semidefinite programming problem with a rank constraint. We propose a new method for solving such SNL problems. We factorize a semidefinite matrix with the rank…

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…

Submodular functions, defined on continuous or discrete domains, arise in numerous applications. We study the minimization of the difference of two submodular (DS) functions, over both domains, extending prior work restricted to set…

We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…

Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…

Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…

Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…

We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…

Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of…

We develop a framework for the distributed minimization of submodular functions. Submodular functions are a discrete analog of convex functions and are extensively used in large-scale combinatorial optimization problems. While there has…

In this paper, we propose the first exact algorithm for minimizing the difference of two submodular functions (D.S.), i.e., the discrete version of the D.C. programming problem. The developed algorithm is a branch-and-bound-based algorithm…

Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization (QDSFM), which allows to model a number of learning tasks on graphs and hypergraphs. The problem exhibits close ties to…

Decentralized learning has been studied intensively in recent years motivated by its wide applications in the context of federated learning. The majority of previous research focuses on the offline setting in which the objective function is…

In this paper, we propose a general algorithmic framework to solve a class of optimization problems on the product of complex Stiefel manifolds based on the matrix polar decomposition. We establish the weak convergence, global convergence…

There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…

Given a collection of monotone submodular functions, the goal of Two-Stage Submodular Maximization (2SSM) [Balkanski et al., 2016] is to restrict the ground set so an objective selected u.a.r. from the collection attains a high maximal…