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Related papers: Supermodular Approximation of Norms and Applicatio…

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In recent years, there have been significant advances in efficiently solving $\ell_s$-regression using linear system solvers and $\ell_2$-regression [Adil-Kyng-Peng-Sachdeva, J. ACM'24]. Would efficient smoothed $\ell_p$-norm solvers lead…

Optimization and Control · Mathematics 2026-01-16 Deeksha Adil , Brian Bullins , Arun Jambulapati , Aaron Sidford

In this paper, we propose scalable methods for maximizing a regularized submodular function $f = g - \ell$ expressed as the difference between a monotone submodular function $g$ and a modular function $\ell$. Indeed, submodularity is…

Machine Learning · Computer Science 2020-02-11 Ehsan Kazemi , Shervin Minaee , Moran Feldman , Amin Karbasi

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…

Discrete Mathematics · Computer Science 2017-07-17 Lin Chen , Moran Feldman , Amin Karbasi

Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest,…

Machine Learning · Computer Science 2020-06-03 Aytunc Sahin , Yatao Bian , Joachim M. Buhmann , Andreas Krause

Consider a variant of the Mastermind game in which queries are $\ell_p$ distances, rather than the usual Hamming distance. That is, a codemaker chooses a hidden vector $\mathbf{y}\in\{-k,-k+1,\dots,k-1,k\}^n$ and answers to queries of the…

Data Structures and Algorithms · Computer Science 2019-09-25 Manuel Fernandez , David P. Woodruff , Taisuke Yasuda

The remarkable successes of neural networks in a huge variety of inverse problems have fueled their adoption in disciplines ranging from medical imaging to seismic analysis over the past decade. However, the high dimensionality of such…

Machine Learning · Statistics 2023-10-11 Santhosh Karnik , Rongrong Wang , Mark Iwen

In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…

Data Structures and Algorithms · Computer Science 2018-03-19 Marko Mitrovic , Moran Feldman , Andreas Krause , Amin Karbasi

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 address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on…

Machine Learning · Computer Science 2012-10-23 Purushottam Kar , Prateek Jain

We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions.…

Computational Complexity · Computer Science 2025-06-16 Aras Bacho , Martin Ziegler

Maximizing submodular functions have been studied extensively for a wide range of subset-selection problems. However, much less attention has been given to the role of submodularity in sequence-selection and ranking problems. A…

Data Structures and Algorithms · Computer Science 2023-01-18 Guangyi Zhang , Nikolaj Tatti , Aristides Gionis

Submodular functions play a key role in the area of optimization as they allow to model many real-world problems that face diminishing returns. Evolutionary algorithms have been shown to obtain strong theoretical performance guarantees for…

In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…

Data Structures and Algorithms · Computer Science 2020-12-22 Wenxin Li

We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when…

Machine Learning · Computer Science 2010-09-02 Julien Mairal , Rodolphe Jenatton , Guillaume Obozinski , Francis Bach

We characterize the streaming space complexity of every symmetric norm $l$ (a norm on $\mathbb{R}^n$ invariant under sign-flips and coordinate-permutations), by relating this space complexity to the measure-concentration characteristics of…

Data Structures and Algorithms · Computer Science 2017-06-27 Jaroslaw Blasiok , Vladimir Braverman , Stephen R. Chestnut , Robert Krauthgamer , Lin F. Yang

Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at…

Optimization and Control · Mathematics 2026-01-27 Jan Schröder , Yair Censor , Philipp Süss , Karl-Heinz Küfer

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…

Data Structures and Algorithms · Computer Science 2015-11-24 Ger Yang , Evdokia Nikolova

In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or…

Optimization and Control · Mathematics 2017-11-01 Vasileios Tzoumas , Konstantinos Gatsis , Ali Jadbabaie , George J. Pappas

We develop polynomial-time algorithms for the fair and efficient allocation of indivisible goods among $n$ agents that have subadditive valuations over the goods. We first consider the Nash social welfare as our objective and design a…

Computer Science and Game Theory · Computer Science 2020-07-07 Siddharth Barman , Umang Bhaskar , Anand Krishna , Ranjani G. Sundaram

This work provides performance guarantees for the greedy solution of experimental design problems. In particular, it focuses on A- and E-optimal designs, for which typical guarantees do not apply since the mean-square error and the maximum…

Machine Learning · Computer Science 2018-02-01 Luiz F. O. Chamon , Alejandro Ribeiro