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Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…

Optimization and Control · Mathematics 2024-01-26 Andreas Löhne

Shifted combinatorial optimization is a new nonlinear optimization framework which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. This framework captures well…

Computational Complexity · Computer Science 2021-02-25 Jakub Gajarský , Petr Hliněný , Martin Koutecký , Shmuel Onn

Interpretable Machine Learning faces a recurring challenge of explaining the predictions made by opaque classifiers such as ensemble models, kernel methods, or neural networks in terms that are understandable to humans. When the model is…

Machine Learning · Computer Science 2024-11-14 Frederic Koriche , Jean-Marie Lagniez , Stefan Mengel , Chi Tran

Optimal feedback control with implicit Hamiltonians poses a fundamental challenge for learning-based value function methods due to the absence of closed-form optimal control laws. Recent work~\cite{gelphman2025end} introduced an implicit…

Optimization and Control · Mathematics 2026-04-28 Eric Gelphman , Deepanshu Verma , Nicole Tianjiao Yang , Stanley Osher , Samy Wu Fung

Constraint programming is used for a variety of real-world optimisation problems, such as planning, scheduling and resource allocation problems. At the same time, one continuously gathers vast amounts of data about these problems. Current…

We define an online learning and optimization problem with discrete and irreversible decisions contributing toward a coverage target. In each period, a decision-maker selects facilities to open, receives information on the success of each…

Machine Learning · Computer Science 2026-03-06 Alexandre Jacquillat , Michael Lingzhi Li

In this work, we introduce the concept of Active Representation Learning, a novel class of problems that intertwines exploration and representation learning within partially observable environments. We extend ideas from Active Simultaneous…

Machine Learning · Computer Science 2024-11-07 Nikola Milosevic , Gesine Müller , Jan Huisken , Nico Scherf

Despite decades of research, existing navigation systems still face real-world challenges when deployed in the wild, e.g., in cluttered home environments or in human-occupied public spaces. To address this, we present a new class of…

We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree (number of occurrences) of variables in various forms of redundancy-free boolean conjunctive normal forms…

Combinatorics · Mathematics 2017-01-24 Oliver Kullmann , Xishun Zhao

In the stochastic submodular cover problem, the goal is to select a subset of stochastic items of minimum expected cost to cover a submodular function. Solutions in this setting correspond to sequential decision processes that select items…

Data Structures and Algorithms · Computer Science 2021-07-01 Rohan Ghuge , Anupam Gupta , Viswanath Nagarajan

This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…

Data Structures and Algorithms · Computer Science 2022-09-13 Nate Veldt

Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…

Systems and Control · Electrical Eng. & Systems 2025-08-12 Alexandros E. Tzikas , Lukas Fiechtner , Arec Jamgochian , Mykel J. Kochenderfer

Given a binary dominance relation on a set of alternatives, a common thread in the social sciences is to identify subsets of alternatives that satisfy certain notions of stability. Examples can be found in areas as diverse as voting theory,…

Computational Complexity · Computer Science 2015-02-06 Dorothea Baumeister , Felix Brandt , Felix Fischer , Jan Hoffmann , Joerg Rothe

Consider the problem of covertly controlling a linear system. In this problem, Alice desires to control (stabilize or change the parameters of) a linear system, while keeping an observer, Willie, unable to decide if the system is indeed…

Optimization and Control · Mathematics 2022-02-15 Barak Amihood , Asaf Cohen

Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…

Machine Learning · Computer Science 2021-02-23 David W. Zhang , Gertjan J. Burghouts , Cees G. M. Snoek

Adversarial training is often formulated as a min-max problem, however, concentrating only on the worst adversarial examples causes alternating repetitive confusion of the model, i.e., previously defended or correctly classified samples are…

Machine Learning · Computer Science 2023-12-13 Qian Li , Yuxiao Hu , Yinpeng Dong , Dongxiao Zhang , Yuntian Chen

We are concerned with the vulnerability of computer vision models to distributional shifts. We formulate a combinatorial optimization problem that allows evaluating the regions in the image space where a given model is more vulnerable, in…

Machine Learning · Computer Science 2019-08-21 Riccardo Volpi , Vittorio Murino

Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…

Machine Learning · Computer Science 2020-01-28 Rishabh Iyer

Impartial selection problems are concerned with the selection of one or more agents from a set based on mutual nominations from within the set. To avoid strategic nominations of the agents, the axiom of impartiality requires that the…

Computer Science and Game Theory · Computer Science 2024-10-01 Javier Cembrano , Max Klimm , Arturo Merino

Many set selection and ranking algorithms have recently been enhanced with diversity constraints that aim to explicitly increase representation of historically disadvantaged populations, or to improve the overall representativeness of the…

Artificial Intelligence · Computer Science 2019-06-06 Ke Yang , Vasilis Gkatzelis , Julia Stoyanovich
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