Related papers: Data Summarization beyond Monotonicity: Non-monoto…

In this paper, we present a thorough study of maximizing a regularized non-monotone submodular function subject to various constraints, i.e., $\max \{ g(A) - \ell(A) : A \in \mathcal{F} \}$, where $g \colon 2^\Omega \to \mathbb{R}_+$ is a…

Cardinality constrained submodular function maximization, which aims to select a subset of size at most $k$ to maximize a monotone submodular utility function, is the key in many data mining and machine learning applications such as data…

Generalizing from a single labeled source domain to unseen target domains, without access to any target data during training, remains a fundamental challenge in robust machine learning. We address this underexplored setting, known as Single…

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…

Meta-Learning has gained increasing attention in the machine learning and artificial intelligence communities. In this paper, we introduce and study an adaptive submodular meta-learning problem. The input of our problem is a set of items,…

We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…

Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…

In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…

We consider the optimal coverage problem where a multi-agent network is deployed in an environment with obstacles to maximize a joint event detection probability. The objective function of this problem is non-convex and no global optimum is…

The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known…

A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…

Submodularity in combinatorial optimization has been a topic of many studies and various algorithmic techniques exploiting submodularity of a studied problem have been proposed. It is therefore natural to ask, in cases where the cost…

Submodular functions are a broad class of set functions, which naturally arise in diverse areas. Many algorithms have been suggested for the maximization of these functions. Unfortunately, once the function deviates from submodularity, the…

We investigate the existence of approximation algorithms for maximization of submodular functions, that run in fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function $v: 2^X \to \mathbb{R}$ the goal is to…

We show that for the problem of minimizing (or maximizing) the ratio of two supermodular functions, no bounded approximation ratio can be achieved via polynomial number of queries, if the two supermodular functions are both monotone…

Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…

Significant development of communication technology over the past few years has motivated research in multi-modal summarization techniques. A majority of the previous works on multi-modal summarization focus on text and images. In this…

We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…

Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete…

We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [FOCS'07] showed a 2/5-approximation for the unconstrained problem and also proved that no…