Related papers: Maximizing the Smallest Eigenvalue of a Symmetric …
We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also…
Distributed maximization of a submodular function in the MapReduce (MR) model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long…
The goal of a sequential decision making problem is to design an interactive policy that adaptively selects a group of items, each selection is based on the feedback from the past, in order to maximize the expected utility of selected…
Submodular optimization is a fundamental problem with many applications in machine learning, often involving decision-making over datasets with sensitive attributes such as gender or age. In such settings, it is often desirable to produce a…
We consider a class of distributed submodular maximization problems in which each agent must choose a single strategy from its strategy set. The global objective is to maximize a submodular function of the strategies chosen by each agent.…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic…
Lower bounds on the smallest eigenvalue of a symmetric positive definite matrices $A\in\mathbb{R}^{m\times m}$ play an important role in condition number estimation and in iterative methods for singular value computation. In particular, the…
In this paper, we present an inexact Noda iteration with inner-outer iterations for finding the smallest eigenvalue and the associated eigenvector of an irreducible monotone matrix. The proposed inexact Noda iteration contains two main…
In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…
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…
Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race.…
We prove an optimal estimate on the smallest singular value of a random subgaussian matrix, valid for all fixed dimensions. For an N by n matrix A with independent and identically distributed subgaussian entries, the smallest singular value…
The problem of maximizing non-negative submodular functions has been studied extensively in the last few years. However, most papers consider submodular set functions. Recently, several advances have been made for the more general case of…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
We study the problem of maximizing a non-monotone, non-negative submodular function subject to a matroid constraint. The prior best-known deterministic approximation ratio for this problem is $\frac{1}{4}-\epsilon$ under…
We consider the actuator placement problem for linear systems. Specifically, we aim to identify an actuator which requires the least amount of control energy to drive the system from an arbitrary initial condition to the origin in the worst…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite…
Submodular maximization arises in many applications, and has attracted a lot of research attentions from various areas such as artificial intelligence, finance and operations research. Previous studies mainly consider only one kind of…