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We study the problem of maximizing a monotone submodular function subject to a cardinality constraint $k$, with the added twist that a number of items $\tau$ from the returned set may be removed. We focus on the worst-case setting…

Machine Learning · Statistics 2017-06-16 Ilija Bogunovic , Slobodan Mitrović , Jonathan Scarlett , Volkan Cevher

The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited…

Data Structures and Algorithms · Computer Science 2019-10-15 Dmitrii Avdiukhin , Grigory Yaroslavtsev , Samson Zhou

We consider the problem of maximizing a monotone submodular function under noise. There has been a great deal of work on optimization of submodular functions under various constraints, resulting in algorithms that provide desirable…

Data Structures and Algorithms · Computer Science 2016-11-08 Avinatan Hassidim , Yaron Singer

We study the classical problem of maximizing a monotone submodular function subject to a cardinality constraint k, with two additional twists: (i) elements arrive in a streaming fashion, and (ii) m items from the algorithm's memory are…

Data Structures and Algorithms · Computer Science 2017-11-27 Slobodan Mitrović , Ilija Bogunovic , Ashkan Norouzi-Fard , Jakub Tarnawski , Volkan Cevher

Uncertainty about models and data is ubiquitous in the computational social sciences, and it creates a need for robust social network algorithms, which can simultaneously provide guarantees across a spectrum of models and parameter…

Social and Information Networks · Computer Science 2016-06-13 Xinran He , David Kempe

In this paper, we study the adversarial robustness of subspace learning problems. Different from the assumptions made in existing work on robust subspace learning where data samples are contaminated by gross sparse outliers or small dense…

Signal Processing · Electrical Eng. & Systems 2020-04-22 Fuwei Li , Lifeng Lai , Shuguang Cui

A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…

Machine Learning · Statistics 2016-06-01 Mario Lucic , Olivier Bachem , Morteza Zadimoghaddam , Andreas Krause

Semi-online algorithms that are allowed to perform a bounded amount of repacking achieve guaranteed good worst-case behaviour in a more realistic setting. Most of the previous works focused on minimization problems that aim to minimize some…

Data Structures and Algorithms · Computer Science 2021-04-21 Sebastian Berndt , Kilian Grage , Klaus Jansen , Lukas Johannsen , Maria Kosche

We study the problem of predicting a set or list of options under knapsack constraint. The quality of such lists are evaluated by a submodular reward function that measures both quality and diversity. Similar to DAgger (Ross et al., 2010),…

Machine Learning · Computer Science 2014-03-18 Jiaji Zhou , Stephane Ross , Yisong Yue , Debadeepta Dey , J. Andrew Bagnell

We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the…

Data Structures and Algorithms · Computer Science 2022-02-09 Andrew Downie , Bahman Gharesifard , Stephen L. Smith

We consider a robust formulation, introduced by Krause et al. (2008), of the classical cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness…

Data Structures and Algorithms · Computer Science 2018-10-31 James B. Orlin , Andreas S. Schulz , Rajan Udwani

In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible…

Optimization and Control · Mathematics 2023-08-16 Jannis Kurtz

We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a nondecreasing submodular…

Data Structures and Algorithms · Computer Science 2014-12-15 Maxim Sviridenko , Jan Vondrák , Justin Ward

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

Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…

Optimization and Control · Mathematics 2020-12-01 Navid Rezazadeh , Solmaz S. Kia

In this paper, we study the \underline{R}obust \underline{o}ptimization for \underline{se}quence \underline{Net}worked \underline{s}ubmodular maximization (RoseNets) problem. We interweave the robust optimization with the sequence networked…

Artificial Intelligence · Computer Science 2023-01-27 Qihao Shi , Bingyang Fu , Can Wang , Jiawei Chen , Sheng Zhou , Yan Feng , Chun Chen

A $k$-submodular function is an extension of a submodular function in that its input is given by $k$ disjoint subsets instead of a single subset. For unconstrained nonnegative $k$-submodular maximization, Ward and \v{Z}ivn\'y proposed a…

Data Structures and Algorithms · Computer Science 2016-08-23 Shinsaku Sakaue

Maximizing a submodular function is a fundamental task in machine learning and 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 of the…

Data Structures and Algorithms · Computer Science 2025-05-26 Paul Dütting , Federico Fusco , Silvio Lattanzi , Ashkan Norouzi-Fard , Morteza Zadimoghaddam

Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…

Data Structures and Algorithms · Computer Science 2025-05-26 Paul Dütting , Federico Fusco , Silvio Lattanzi , Ashkan Norouzi-Fard , Morteza Zadimoghaddam

This paper studies online nonstochastic control problems with adversarial and static constraints. We propose online nonstochastic control algorithms that achieve both sublinear regret and sublinear adversarial constraint violation while…

Machine Learning · Computer Science 2023-02-07 Xin Liu , Zixian Yang , Lei Ying
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