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We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…

Machine Learning · Computer Science 2010-10-22 Kenneth L. Clarkson , Elad Hazan , David P. Woodruff

In this work, we study the classical problem of maximizing a submodular function subject to a matroid constraint. We develop deterministic algorithms that are very parsimonious with respect to querying the submodular function, for both the…

Data Structures and Algorithms · Computer Science 2024-08-29 Eric Balkanski , Steven DiSilvio , Alan Kuhnle , ChunLi Peng

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…

Machine Learning · Computer Science 2017-11-07 Mohammad Reza Karimi , Mario Lucic , Hamed Hassani , Andreas Krause

We consider non-monotone DR-submodular function maximization, where DR-submodularity (diminishing return submodularity) is an extension of submodularity for functions over the integer lattice based on the concept of the diminishing return…

Data Structures and Algorithms · Computer Science 2016-12-06 Tasuku Soma , Yuichi Yoshida

Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less…

Data Structures and Algorithms · Computer Science 2010-10-07 Anupam Gupta , Aaron Roth , Grant Schoenebeck , Kunal Talwar

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

Mini-batch gradient descent based methods are the de facto algorithms for training neural network architectures today. We introduce a mini-batch selection strategy based on submodular function maximization. Our novel submodular formulation…

Machine Learning · Computer Science 2019-06-21 K J Joseph , Vamshi Teja R , Krishnakant Singh , Vineeth N Balasubramanian

We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…

Discrete Mathematics · Computer Science 2019-02-22 Tobias Friedrich , Andreas Göbel , Frank Neumann , Francesco Quinzan , Ralf Rothenberger

Maximizing submodular objectives under constraints is a fundamental problem in machine learning and optimization. We study the maximization of a nonnegative, non-monotone $\gamma$-weakly DR-submodular function over a down-closed convex…

Machine Learning · Computer Science 2026-01-05 Hareshkumar Jadav , Ranveer Singh , Vaneet Aggarwal

It is generally believed that submodular functions -- and the more general class of $\gamma$-weakly submodular functions -- may only be optimized under the non-negativity assumption $f(S) \geq 0$. In this paper, we show that once the…

Data Structures and Algorithms · Computer Science 2019-04-23 Christopher Harshaw , Moran Feldman , Justin Ward , Amin Karbasi

The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a $1-1/e$ factor. Although it is well known that this guarantee is essentially…

Data Structures and Algorithms · Computer Science 2022-02-15 Aviad Rubinstein , Junyao Zhao

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

We describe a parallel approximation algorithm for maximizing monotone submodular functions subject to hereditary constraints on distributed memory multiprocessors. Our work is motivated by the need to solve submodular optimization problems…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-02-18 Shivaram Gopal , S M Ferdous , Hemanta K. Maji , Alex Pothen

The virtualization and softwarization of modern computer networks introduces interesting new opportunities for a more flexible placement of network functions and middleboxes (firewalls, proxies, traffic optimizers, virtual switches, etc.).…

Networking and Internet Architecture · Computer Science 2017-06-21 Tamas Lukovszki , Matthias Rost , Stefan Schmid

We consider the problem of maximizing submodular functions; while this problem is known to be NP-hard, several numerically efficient local search techniques with approximation guarantees are available. In this paper, we propose a novel…

Machine Learning · Computer Science 2013-09-11 K. S. Sesh Kumar , Francis Bach

Real continuous submodular functions, as a generalization of the corresponding discrete notion to the continuous domain, gained considerable attention recently. The analog notion for entropy functions requires additional properties: a real…

Optimization and Control · Mathematics 2021-02-12 Laszlo Csirmaz

We introduce the problem of maximizing approximately $k$-submodular functions subject to size constraints. In this problem, one seeks to select $k$-disjoint subsets of a ground set with bounded total size or individual sizes, and maximum…

Data Structures and Algorithms · Computer Science 2021-01-19 Leqian Zheng , Hau Chan , Grigorios Loukides , Minming Li

Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary…

Data Structures and Algorithms · Computer Science 2024-02-20 Paul Dütting , Federico Fusco , Silvio Lattanzi , Ashkan Norouzi-Fard , Morteza Zadimoghaddam

Many real-world optimization problems can be stated in terms of submodular functions. Furthermore, these real-world problems often involve uncertainties which may lead to the violation of given constraints. A lot of evolutionary…

Neural and Evolutionary Computing · Computer Science 2024-11-04 Aneta Neumann , Frank Neumann

Submodular maximization under matroid and cardinality constraints are classical problems with a wide range of applications in machine learning, auction theory, and combinatorial optimization. In this paper, we consider these problems in the…

Data Structures and Algorithms · Computer Science 2023-12-27 Kiarash Banihashem , Leyla Biabani , Samira Goudarzi , MohammadTaghi Hajiaghayi , Peyman Jabbarzade , Morteza Monemizadeh