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Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…

Data Structures and Algorithms · Computer Science 2012-08-24 Maria-Florina Balcan , Nicholas J. A. Harvey

Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…

Optimization and Control · Mathematics 2021-11-03 Arman Adibi , Aryan Mokhtari , Hamed Hassani

We study the probabilistic assignment of items to platforms that satisfies both group and individual fairness constraints. Each item belongs to specific groups and has a preference ordering over platforms. Each platform enforces group…

Artificial Intelligence · Computer Science 2024-05-13 Atasi Panda , Anand Louis , Prajakta Nimbhorkar

We demonstrate the usefulness of submodularity in statistics as a characterization of the difficulty of the \emph{search} problem of feature selection. The search problem is the ability of a procedure to identify an informative set of…

Statistics Theory · Mathematics 2016-05-16 Kory D. Johnson , Robert A. Stine , Dean P. Foster

Submodular optimization finds applications in machine learning and data mining. In this paper, we study the problem of maximizing functions of the form $h = f-c$, where $f$ is a monotone, non-negative, weakly submodular set function and $c$…

Data Structures and Algorithms · Computer Science 2024-08-20 Yanhui Zhu , Samik Basu , A. Pavan

Many large-scale machine learning problems--clustering, non-parametric learning, kernel machines, etc.--require selecting a small yet representative subset from a large dataset. Such problems can often be reduced to maximizing a submodular…

Machine Learning · Computer Science 2016-06-28 Baharan Mirzasoleiman , Amin Karbasi , Rik Sarkar , Andreas Krause

Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location and marketing over social networks. In this paper we…

Data Structures and Algorithms · Computer Science 2011-01-18 Ariel Kulik , Hadas Shachnai , Tami Tamir

Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions,…

Discrete Mathematics · Computer Science 2014-11-18 Allan Borodin , Dai Tri Man Le , Yuli Ye

Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this…

Data Structures and Algorithms · Computer Science 2016-11-01 Alessandro Epasto , Silvio Lattanzi , Sergei Vassilvitskii , Morteza Zadimoghaddam

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…

Data Structures and Algorithms · Computer Science 2022-09-13 Shaojie Tang

In recent years, fairness in machine learning has emerged as a critical concern to ensure that developed and deployed predictive models do not have disadvantageous predictions for marginalized groups. It is essential to mitigate…

Machine Learning · Computer Science 2025-04-18 Jansen S. B. Pereira , Giovani Valdrighi , Marcos Medeiros Raimundo

Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…

Data Structures and Algorithms · Computer Science 2026-02-19 Ajitesh Srivastava , Shanghua Teng

The sheer scale of modern datasets has resulted in a dire need for summarization techniques that identify representative elements in a dataset. Fortunately, the vast majority of data summarization tasks satisfy an intuitive diminishing…

Machine Learning · Computer Science 2018-06-08 Marko Mitrovic , Ehsan Kazemi , Morteza Zadimoghaddam , Amin Karbasi

We consider robust submodular maximization problems (RSMs), where given a set of $m$ monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes…

Optimization and Control · Mathematics 2023-06-12 Hsin-Yi Huang , Hao-Hsiang Wu , Simge Kucukyavuz

We study the following problem: Given a variable of interest, we would like to find a best linear predictor for it by choosing a subset of $k$ relevant variables obeying a matroid constraint. This problem is a natural generalization of…

Data Structures and Algorithms · Computer Science 2023-01-19 Theophile Thiery , Justin Ward

Influence maximization is a widely used model for information dissemination in social networks. Recent work has employed such interventions across a wide range of social problems, spanning public health, substance abuse, and international…

Computer Science and Game Theory · Computer Science 2019-03-27 Alan Tsang , Bryan Wilder , Eric Rice , Milind Tambe , Yair Zick

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

Machine Learning · Computer Science 2015-02-10 Alina Ene , Huy L. Nguyen

In this paper, we study the problem of fair worker selection in Federated Learning systems, where fairness serves as an incentive mechanism that encourages more workers to participate in the federation. Considering the achieved training…

Computer Science and Game Theory · Computer Science 2021-07-27 Fengjiao Li , Jia Liu , Bo Ji

We study two mixed robust/average-case submodular partitioning problems that we collectively call Submodular Partitioning. These problems generalize both purely robust instances of the problem (namely max-min submodular fair allocation…

Data Structures and Algorithms · Computer Science 2016-08-17 Kai Wei , Rishabh Iyer , Shengjie Wang , Wenruo Bai , Jeff Bilmes

We address the problem of maximizing an unknown submodular function that can only be accessed via noisy evaluations. Our work is motivated by the task of summarizing content, e.g., image collections, by leveraging users' feedback in form of…

Artificial Intelligence · Computer Science 2015-12-02 Adish Singla , Sebastian Tschiatschek , Andreas Krause
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