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In this work we give two new algorithms that use similar techniques for (non-monotone) submodular function maximization subject to a cardinality constraint. The first is an offline fixed parameter tractable algorithm that guarantees a…

Data Structures and Algorithms · Computer Science 2022-04-26 Aviad Rubinstein , Junyao Zhao

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…

Machine Learning · Computer Science 2024-07-09 Wenjing Chen , Shuo Xing , Samson Zhou , Victoria G. Crawford

Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of…

Data Structures and Algorithms · Computer Science 2020-02-12 Alfredo Torrico , Mohit Singh , Sebastian Pokutta

We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…

Optimization and Control · Mathematics 2026-02-12 Ching-pei Lee , Stephen J. Wright

Maximizing submodular functions has been increasingly used in many applications of machine learning, such as data summarization, recommendation systems, and feature selection. Moreover, there has been a growing interest in both submodular…

Data Structures and Algorithms · Computer Science 2023-11-08 Kiarash Banihashem , Leyla Biabani , Samira Goudarzi , MohammadTaghi Hajiaghayi , Peyman Jabbarzade , Morteza Monemizadeh

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

Optimization and Control · Mathematics 2020-03-10 Ion Necoara

We show that the recent breakthrough result of [Buchbinder and Feldman, FOCS'24] could further lead to a deterministic $(1-\kappa_{f}/e-\varepsilon)$-approximate algorithm for maximizing a submodular function with curvature $\kappa_{f}$…

Data Structures and Algorithms · Computer Science 2024-09-06 Wenxin Li

The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…

Data Structures and Algorithms · Computer Science 2017-12-01 Simon Bruggmann , Rico Zenklusen

Maximization of {\it non-submodular} functions appears in various scenarios, and many previous works studied it based on some measures that quantify the closeness to being submodular. On the other hand, many practical non-submodular…

Data Structures and Algorithms · Computer Science 2019-10-04 Shinsaku Sakaue

The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…

Data Structures and Algorithms · Computer Science 2018-10-31 Nived Rajaraman , Rahul Vaze

Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…

Data Structures and Algorithms · Computer Science 2013-04-19 Nikhil R. Devanur , Shaddin Dughmi , Roy Schwartz , Ankit Sharma , Mohit Singh

This paper studies the problem of maximizing a monotone submodular function under an unknown knapsack constraint. A solution to this problem is a policy that decides which item to pack next based on the past packing history. The robustness…

Data Structures and Algorithms · Computer Science 2024-10-25 Max Klimm , Martin Knaack

We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This…

Machine Learning · Statistics 2014-05-14 Anastasios Kyrillidis , Rabeeh Karimi Mahabadi , Quoc Tran-Dinh , Volkan Cevher

Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…

Data Structures and Algorithms · Computer Science 2011-11-08 Shaddin Dughmi

The usual approach to developing and analyzing first-order methods for non-smooth (stochastic or deterministic) convex optimization assumes that the objective function is uniformly Lipschitz continuous with parameter $M_f$. However, in many…

Optimization and Control · Mathematics 2018-08-15 Haihao Lu

The standard greedy algorithm has been recently shown to enjoy approximation guarantees for constrained non-submodular nondecreasing set function maximization. While these recent results allow to better characterize the empirical success of…

Social and Information Networks · Computer Science 2019-10-09 Khashayar Gatmiry , Manuel Gomez-Rodriguez

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…

Information Theory · Computer Science 2017-09-18 Andrea Simonetto , Aryan Mokhtari , Alec Koppel , Geert Leus , Alejandro Ribeiro

In this paper we describe a new algorithm called Fast Adaptive Sequencing Technique (FAST) for maximizing a monotone submodular function under a cardinality constraint $k$ whose approximation ratio is arbitrarily close to $1-1/e$, is…

Machine Learning · Computer Science 2019-07-16 Adam Breuer , Eric Balkanski , Yaron Singer

This paper proposes a novel first-order algorithm that solves composite nonsmooth and stochastic convex optimization problem with function constraints. Most of the works in the literature provide convergence rate guarantees on the…

Optimization and Control · Mathematics 2024-10-25 Digvijay Boob , Mohammad Khalafi

Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…

Optimization and Control · Mathematics 2023-05-23 Oisín Faust , Hamza Fawzi