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Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…

Analysis of PDEs · Mathematics 2016-10-04 Diogo A. Gomes , Stefania Patrizi

We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is…

Multiagent Systems · Computer Science 2021-05-18 Sarah Perrin , Mathieu Laurière , Julien Pérolat , Matthieu Geist , Romuald Élie , Olivier Pietquin

Alternating minimization represents a widely applicable and empirically successful approach for finding low-rank matrices that best fit the given data. For example, for the problem of low-rank matrix completion, this method is believed to…

Machine Learning · Statistics 2012-12-04 Prateek Jain , Praneeth Netrapalli , Sujay Sanghavi

Partial set cover problem and set multi-cover problem are two generalizations of set cover problem. In this paper, we consider the partial set multi-cover problem which is a combination of them: given an element set $E$, a collection of…

Discrete Mathematics · Computer Science 2019-07-05 Yishuo Shi , Yingli Ran , Zhao Zhang , James Willson , Guangmo Tong , Ding-Zhu Du

The problem of coverage control, i.e., of coordinating multiple agents to optimally cover an area, arises in various applications. However, coverage applications face two major challenges: (1) dealing with nonlinear dynamics while…

Systems and Control · Electrical Eng. & Systems 2024-04-01 Rahel Rickenbach , Johannes Köhler , Anna Scampicchio , Melanie N. Zeilinger , Andrea Carron

Running time of the light field depth estimation algorithms is typically high. This assessment is based on the computational complexity of existing methods and the large amounts of data involved. The aim of our work is to develop a simple…

Computer Vision and Pattern Recognition · Computer Science 2019-08-01 Yuriy Anisimov , Oliver Wasenmüller , Didier Stricker

Mean field approximation is a powerful technique which has been used in many settings to study large-scale stochastic systems. In the case of two-timescale systems, the approximation is obtained by a combination of scaling arguments and the…

Probability · Mathematics 2023-01-24 Sebastian Allmeier , Nicolas Gast

Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI.…

Artificial Intelligence · Computer Science 2021-02-04 Alexey Ignatiev , Edward Lam , Peter J. Stuckey , Joao Marques-Silva

In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…

Data Structures and Algorithms · Computer Science 2018-07-26 Hossein Esfandiari , Michael Mitzenmacher

Finding an energy minimum in the Ising model is an exemplar objective, associated with many combinatorial optimization problems, that is computationally hard in general, but occurs in all areas of modern science. There are several numerical…

Quantum Physics · Physics 2019-07-17 A. Yavorsky , L. A. Markovich , E. A. Polyakov , A. N. Rubtsov

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

Optimization and Control · Mathematics 2020-07-23 Lisang Ding , Wuchen Li , Stanley Osher , Wotao Yin

We investigate reinforcement learning in the setting of Markov decision processes for a large number of exchangeable agents interacting in a mean field manner. Applications include, for example, the control of a large number of robots…

Optimization and Control · Mathematics 2025-04-30 René Carmona , Mathieu Laurière , Zongjun Tan

This paper is devoted to the numerical resolution of McKean-Vlasov control problems via the class of mean-field neural networks introduced in our companion paper [25] in order to learn the solution on the Wasserstein space. We propose…

Optimization and Control · Mathematics 2024-03-20 Huyên Pham , Xavier Warin

This paper addresses optimal feedback selection for generic arbitrary pole placement of structured systems when each feedback edge is associated with a cost. Given a structured system and a feedback cost matrix, our aim is to find a…

Optimization and Control · Mathematics 2017-07-06 Shana Moothedath , Prasanna Chaporkar , Madhu N. Belur

A novel method is presented and explored within the framework of Potts neural networks for solving optimization problems with a non-trivial topology, with the airline crew scheduling problem as a target application. The key ingredient to…

Disordered Systems and Neural Networks · Physics 2016-08-15 M. Lagerholm , C. Peterson , B. Söderberg

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to…

Optimization and Control · Mathematics 2024-12-18 Lijun Bo , Dongfang Yang , Shihua Wang

Minimum connected dominating set problem is an NP-hard combinatorial optimization problem in graph theory. Finding connected dominating set is of high interest in various domains such as wireless sensor networks, optical networks, and…

Artificial Intelligence · Computer Science 2024-05-28 Hayet Dahmri , Salim Bouamama

This paper describes a novel method to solve average-reward semi-Markov decision processes, by reducing them to a minimal sequence of cumulative reward problems. The usual solution methods for this type of problems update the gain (optimal…

Machine Learning · Computer Science 2015-04-21 Reinaldo Uribe Muriel , Fernando Lozando , Charles Anderson

Mean field control (MFC) problems have been introduced to study social optima in very large populations of strategic agents. The main idea is to consider an infinite population and to simplify the analysis by using a mean field…

Optimization and Control · Mathematics 2023-03-01 Sebastian Baudelet , Brieuc Frénais , Mathieu Laurière , Amal Machtalay , Yuchen Zhu

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…

Optimization and Control · Mathematics 2020-06-09 Yajing Liu , April Sagan , Andrey Bernstein , Rui Yang , Xinyang Zhou , Yingchen Zhang