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Multi-Armed Bandits with Applications to Markov Decision Processes and Scheduling Problems
SSStttooonnnyyy BBBrrrooooookkk UUUnnniiivvveeerrrsssiiitttyyy The official electronic file of this thesis or dissertation is maintained by the University Libraries on behalf of The Graduate School at Stony Brook University. ©©© AAAllllll RRRiiiggghhhtttsss RRReeessseeerrrvvveeeddd bbbyyy AAAuuuttthhhooorrr... Multi-Armed Bandits with Applications to Markov Decision Processes and Scheduling Problems A Dissertation Presented by Isa M. Muqattash to The Graduate School in Partial Ful¯llment of the Requirements for the Degree of Doctor of Philosophy in Applied Mathematics and Statistics (Operations Research) Stony Brook University December 2014 Stony Brook University The Graduate School Isa M. Muqattash We, the dissertation committee for the above candidate for the Doctor of Philosophy degree, hereby recommend acceptance of this dissertation. Jiaqiao Hu { Dissertation Advisor Associate Professor, Department of Applied Mathematics and Statistics Esther Arkin { Chairperson of Defense Professor, Department of Applied Mathematics and Statistics Yuefan Deng Professor, Department of Applied Mathematics and Statistics Luis E. Ortiz Assistant Professor Department of Computer Science, Stony Brook University This dissertation is accepted by the Graduate School. Charles Taber Dean of the Graduate School ii Abstract of the Dissertation Multi-Armed Bandits with Applications to Markov Decision Processes and Scheduling Problems by Isa M. Muqattash Doctor of Philosophy in Applied Mathematics and Statistics (Operations Research) Stony Brook University 2014 The focus of this work is on practical applications of stochastic multi-armed bandits (MABs) in two distinctive settings. First, we develop and present REGA, a novel adaptive sampling- based algorithm for control of ¯nite-horizon Markov decision pro- cesses (MDPs) with very large state spaces and small action spaces. We apply a variant of the ²-greedy multi-armed bandit algorithm to each stage of the MDP in a recursive manner, thus comput- ing an estimation of the \reward-to-go" value at each stage of the MDP. -
Stony Brook University
SSStttooonnnyyy BBBrrrooooookkk UUUnnniiivvveeerrrsssiiitttyyy The official electronic file of this thesis or dissertation is maintained by the University Libraries on behalf of The Graduate School at Stony Brook University. ©©© AAAllllll RRRiiiggghhhtttsss RRReeessseeerrrvvveeeddd bbbyyy AAAuuuttthhhooorrr... Integrating Mobile Agents and Distributed Sensors in Wireless Sensor Networks A Dissertation presented by Jiemin Zeng to The Graduate School in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Computer Science Stony Brook University May 2016 Copyright by Jiemin Zeng 2016 Stony Brook University The Graduate School Jiemin Zeng We, the dissertation committee for the above candidate for the Doctor of Philosophy degree, hereby recommend acceptance of this dissertation Jie Gao - Dissertation Advisor Professor, Computer Science Department Joseph Mitchell - Chairperson of Defense Professor, Department of Applied Mathematics and Statistics Esther Arkin Professor, Department of Applied Mathematics and Statistics Matthew P. Johnson - External Member Assistant Professor Department of Mathematics and Computer Science at Lehman College PhD Program in Computer Science at The CUNY Graduate Center This dissertation is accepted by the Graduate School Charles Taber Dean of the Graduate School ii Abstract of the Dissertation Integrating Mobile Agents and Distributed Sensors in Wireless Sensor Networks by Jiemin Zeng Doctor of Philosophy in Computer Science Stony Brook University 2016 As computers become more ubiquitous in the prominent phenomenon of the In- ternet of Things, we encounter many unique challenges in the field of wireless sensor networks. A wireless sensor network is a group of small, low powered sensors with wireless capability to communicate with each other. The goal of these sensors, also called nodes, generally is to collect some information about their environment and report it back to a base station. -
2Majors and Minors.Qxd.KA
APPLIED MATHEMATICS AND STATISTICS Spring 2007: updates since Fall 2006 are in red Applied Mathematics and Statistics (AMS) Major and Minor in Applied Mathematics and Statistics Department of Applied Mathematics and Statistics, College of Engineering and Applied Sciences CHAIRPERSON: James Glimm UNDERGRADUATE PROGRAM DIRECTOR: Alan C. Tucker UNDERGRADUATE SECRETARY: Elizabeth Ahmad OFFICE: P-139B Math Tower PHONE: (631) 632-8370 E-MAIL: [email protected] WEB ADDRESS: http://naples.cc.sunysb.edu/CEAS/amsweb.nsf Students majoring in Applied Mathematics and Statistics often double major in one of the following: Computer Science (CSE), Economics (ECO), Information Systems (ISE) Faculty Bradley Plohr, Adjunct Professor, Ph.D., he undergraduate program in Princeton University: Conservation laws; com- Hongshik Ahn, Associate Professor, Ph.D., Applied Mathematics and Statistics putational fluid dynamics. University of Wisconsin: Biostatistics; survival Taims to give mathematically ori- analysis. John Reinitz, Professor, Ph.D., Yale University: ented students a liberal education in quan- Mathematical biology. Esther Arkin, Professor, Ph.D., Stanford titative problem solving. The courses in University: Computational geometry; combina- Robert Rizzo, Assistant Professor, Ph.D., Yale this program survey a wide variety of torial optimization. University: Bioinformatics; drug design. mathematical theories and techniques Edward J. Beltrami, Professor Emeritus, Ph.D., David Sharp, Adjunct Professor, Ph.D., that are currently used by analysts and Adelphi University: Optimization; stochastic California Institute of Technology: Mathematical researchers in government, industry, and models. physics. science. Many of the applied mathematics Yung Ming Chen, Professor Emeritus, Ph.D., Ram P. Srivastav, Professor, D.Sc., University of courses give students the opportunity to New York University: Partial differential equa- Glasgow; Ph.D., University of Lucknow: Integral develop problem-solving techniques using equations; numerical solutions. -
Games of Threats
Accepted Manuscript Games of threats Elon Kohlberg, Abraham Neyman PII: S0899-8256(17)30190-2 DOI: https://doi.org/10.1016/j.geb.2017.10.018 Reference: YGAME 2771 To appear in: Games and Economic Behavior Received date: 30 August 2017 Please cite this article in press as: Kohlberg, E., Neyman, A. Games of threats. Games Econ. Behav. (2017), https://doi.org/10.1016/j.geb.2017.10.018 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. GAMES OF THREATS ELON KOHLBERG∗ AND ABRAHAM NEYMAN+ Abstract. Agameofthreatsonafinitesetofplayers,N, is a function d that assigns a real number to any coalition, S ⊆ N, such that d(S)=−d(N \S). A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition d(∅)=0.We show that analogs of the classic Shapley axioms for coalitional games determine a unique value for games of threats. This value assigns to each player an average of d(S)acrossall the coalitions that include the player. Games of threats arise naturally in value theory for strategic games, and may have applications in other branches of game theory. 1. Introduction The Shapley value is the most widely studied solution concept of cooperative game theory. -
DEPARTMENT of ECONOMICS NEWSLETTER Issue #1
DEPARTMENT OF ECONOMICS NEWSLETTER Issue #1 DEPARTMENT OF ECONOMICS SEPTEMBER 2017 STONY BROOK UNIVERSITY IN THIS ISSUE Message from the Chair by Juan Carlos Conesa Greetings from the Department of Regarding news for the coming Economics in the College of Arts and academic year, we are very excited to Sciences at Stony Brook University! announce that David Wiczer, currently Since the beginning of the spring working for the Research Department of semester, we’ve celebrated several the Federal Reserve Bank of St Louis, 2017 Commencement Ceremony accomplishments of both students and will be joining us next semester as an Juan Carlos Conesa, Vincent J. Cassidy (BA ‘81), Anand George (BA ‘02) and Hugo faculty alike. I’d also like to tell you of Assistant Professor. David is an what’s to come for next year. enthusiastic researcher working on the Benitez‐Silva intersection of Macroeconomics and The beginning of 2017 has been a very Labor Economics, with a broad exciting time for our students. Six of our perspective combining theoretical, PhD students started looking for options computational and data analysis. We are to start exciting professional careers. really looking forward to David’s Arda Aktas specializes in Demographics, interaction with both students and and will be moving to a Post‐doctoral faculty alike. We are also happy to position at the World Population welcome Prof. Basak Horowitz, who will Program in the International Institute for join the Economics Department in Fall Applied Systems Analysis (IIASA), in 2017, as a new Lecturer. Basak’s Austria. Anju Bhandari specializes in research interests are microeconomic Macroeconomics, and has accepted a theory, economics of networks and New faculty, David Wiczer position as an Assistant Vice President matching theory, industrial organization with Citibank, NY. -
Games of Threats
Games of Threats The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Kohlberg, Elon, and Abraham Neyman. "Games of Threats." Games and Economic Behavior 108 (March 2018): 139–145. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:39148383 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP GAMES OF THREATS ELON KOHLBERG∗ AND ABRAHAM NEYMAN+ Abstract. Agameofthreatsonafinitesetofplayers,N, is a function d that assigns a real number to any coalition, S ⊆ N, such that d(S)=−d(N \S). A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition d(∅)=0.We show that analogs of the classic Shapley axioms for coalitional games determine a unique value for games of threats. This value assigns to each player an average of d(S)acrossall the coalitions that include the player. Games of threats arise naturally in value theory for strategic games, and may have applications in other branches of game theory. 1. Introduction The Shapley value is the most widely studied solution concept of cooperative game theory. It is defined on coalitional games, which are the standard objects of the theory. A coalitional game on a finite set of players, N, is a function v that assigns a real number to any subset (“coalition”), S ⊆ N, such that v(∅) = 0. -
2018 Unité De Recherche Dossier D'autoévaluation
Évaluation des unités de recherche Novembre 2016 Vague D Campagne d’évaluation 2017 – 2018 Unité de recherche Dossier d’autoévaluation Informations générales Nom de l’unité : Centre de Recherche en Mathématiques de la Décision Acronyme : CEREMADE UMR CNRS 7534 Champ de recherche de rattachement : Recherche Nom du directeur pour le contrat en cours : Vincent Rivoirard Nom du directeur pour le contrat à venir : Vincent Rivoirard Type de demande : Renouvellement à l’identique x Restructuration □ Création ex nihilo □ Établissements et organismes de rattachement : Liste des établissements et organismes tutelles de l’unité de recherche pour le contrat en cours et pour le prochain contrat (tutelles). Contrat en cours : | Prochain contrat : - Université Paris-Dauphine |- Université Paris-Dauphine - CNRS |- CNRS Choix de l’évaluation interdisciplinaire de l’unité de recherche ou de l’équipe interne : Oui □ Non x Vague D : campagne d’évaluation 2017 – 2018 1 Département d’évaluation de la recherche 2 Table des matières 1 Présentation du Ceremade7 1.1 Introduction..............................................7 1.2 Tableau des effectifs et moyens du Ceremade............................7 1.2.1 Effectifs............................................7 1.2.2 Parité.............................................9 1.2.3 Moyens financiers......................................9 1.2.4 Locaux occupés........................................ 10 1.2.5 Ressources documentaires.................................. 10 1.3 Politique scientifique......................................... 10 1.3.1 Missions et objectifs scientifiques.............................. 10 1.3.2 Structuration......................................... 11 1.3.3 Recrutements......................................... 12 1.3.4 Illustration de la mise en œuvre de la stratégie scientifique adoptée en 2012 en direction des applications........................................ 14 1.3.5 Programmes de soutien à la recherche du Ceremade déployés par la Fondation Dauphine, PSL, la FSMP et la Région Ile-de-France......................... -
A Formula for the Value of a Stochastic Game
A formula for the value of a stochastic game Luc Attiaa,1 and Miquel Oliu-Bartonb,1,2 aCentre de Mathematiques´ Appliquees,´ Ecole´ Polytechnique, 91128 Palaiseau, France; and bCentre de Recherches en Mathematiques´ de la Decision,´ Universite´ Paris-Dauphine, Paris Sciences et Lettres, 75016 Paris, France Edited by Robert J. Aumann, The Hebrew University, Jerusalem, Israel, and approved November 12, 2019 (received for review May 21, 2019) In 1953, Lloyd Shapley defined the model of stochastic games, a formula for the value (proved in Section 4). Section 5 describes which were the first general dynamic model of a game to be the algorithmic implications and tractability of these 2 formulas. defined, and proved that competitive stochastic games have a Section 6 concludes with remarks and extensions. discounted value. In 1982, Jean-Franc¸ois Mertens and Abraham Neyman proved that competitive stochastic games admit a robust 2. Context and Main Results solution concept, the value, which is equal to the limit of the To state our results precisely, we recall some definitions and well- discounted values as the discount rate goes to 0. Both contribu- known results about 2-player zero-sum games (Section 2A) and tions were published in PNAS. In the present paper, we provide a about finite competitive stochastic games (Section 2B). In Sec- tractable formula for the value of competitive stochastic games. tion 2C we give a brief overview of the relevant literature on finite competitive stochastic games. Our results are described in stochastic games j repeated games j dynamic programming Section 2D. Notation. Throughout this paper, N denotes the set of positive 1. -
Algorithmica (2006) 46: 193–221 DOI: 10.1007/S00453-006-1206-1 Algorithmica © 2006 Springer Science+Business Media, Inc
Algorithmica (2006) 46: 193–221 DOI: 10.1007/s00453-006-1206-1 Algorithmica © 2006 Springer Science+Business Media, Inc. The Freeze-Tag Problem: How to Wake Up a Swarm of Robots1 Esther M. Arkin,2 Michael A. Bender,3 Sandor´ P. Fekete,4 Joseph S. B. Mitchell,2 and Martin Skutella5 Abstract. An optimization problem that naturally arises in the study of swarm robotics is the Freeze-Tag Problem (FTP) of how to awaken a set of “asleep” robots, by having an awakened robot move to their locations. Once a robot is awake, it can assist in awakening other slumbering robots. The objective is to have all robots awake as early as possible. While the FTP bears some resemblance to problems from areas in combinato- rial optimization such as routing, broadcasting, scheduling, and covering, its algorithmic characteristics are surprisingly different. We consider both scenarios on graphs and in geometric environments. In graphs, robots sleep at vertices and there is a length function on the edges. Awake robots travel along edges, with time depending on edge length. For most scenarios, we consider the offline version of the problem, in which each awake robot knows the position of all other robots. We prove that the problem is NP-hard, even for the special case of star graphs. We also establish hardness of approximation, showing that it is NP-hard to obtain an approximation factor 5 better than 3 , even for graphs of bounded degree. These lower bounds are complemented with several positive algorithmic results, including: We show that the natural greedy strategy on star graphs has a tight worst-case performance of 7 and give • 3 a polynomial-time approximation scheme (PTAS) for star graphs. -
The Freeze-Tag Problem: How to Wake up a Swarm of Robots
The Freeze-Tag Problem: How to Wake Up a Swarm of Robots∗ Esther M. Arkin† Michael A. Bender‡ S´andor P. Fekete§ Joseph S. B. Mitchell† Martin Skutella¶ Abstract An optimization problem that naturally arises in the study of swarm robotics is the Freeze-Tag Problem (FTP) of how to awaken a set of “asleep” robots, by having an awakened robot move to their locations. Once a robot is awake, it can assist in awakening other slumbering robots. The objective is to have all robots awake as early as possible. While the FTP bears some resemblance to problems from areas in combinatorial optimization such as routing, broadcasting, scheduling, and covering, its algorithmic characteristics are surprisingly different. We consider both scenarios on graphs and in geometric environments. In graphs, robots sleep at vertices and there is a length function on the edges. Awake robots travel along edges, with time depending on edge length. For most scenarios, we consider the offline version of the problem, in which each awake robot knows the position of all other robots. We prove that the problem is NP-hard, even for the special case of star graphs. We also establish hardness of approximation, showing that it is NP-hard to obtain an approximation factor better than 5/3, even for graphs of bounded degree. These lower bounds are complemented with several positive algorithmic results, including: We show that the natural greedy strategy on star graphs has a tight worst-case performance of 7/3 • and give a polynomial-time approximation scheme (PTAS) for star graphs. We give a simple O(log ∆)-competitive online algorithm for graphs with maximum degree ∆ and • locally bounded edge weights. -
Special Issue in Honor of Abraham Neyman
Int J Game Theory (2016) 45:3–9 DOI 10.1007/s00182-015-0518-2 PREFACE Special issue in honor of Abraham Neyman Olivier Gossner1 · Ori Haimanko2 · Eilon Solan3 Published online: 16 March 2016 © Springer-Verlag Berlin Heidelberg 2016 Preface The International Journal of Game Theory is proud to publish a special issue in honor of the contributions of Prof. Abraham Neyman to Game Theory. Abraham Neyman graduated from the Hebrew University of Jerusalem in 1977. His dissertaton, titled “Values of Games with a Continuum of Players”, was completed under the supervi- sion of Robert Aumann and was awarded the Aharon Katzir Prize for an Excellent Ph.D. thesis. After graduation he obtained a visiting position at Cornell University, from where he continued on to Berkeley. In 1982 Abraham Neyman joined the Hebrew University of Jerusalem, where he participated in the founding of the Center for the Study of Rationality in 1991. In 1985 he became one of the founders of the Center for Game Theory at Stony Brook University, where he worked for 16 years, in 1989 he was elected as a Fellow of the Econometric Society, and in 1999 he was selected a Charter Member of the Game Theory Society. Abraham Neyman was the advisor of 12 Ph.D. students. He has thus far published 67 articles and co-edited three books. He has also been the co-organizer of numer- ous conferences and workshops. He served as the Area Editor for Game Theory in B Eilon Solan [email protected] Olivier Gossner [email protected] Ori Haimanko [email protected] 1 École Polytechnique - CNRS, France, and London School of Economics, Paris, France, UK 2 Department of Economics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel 3 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 6997800, Israel 123 4 O. -
Network Optimization on Partitioned Pairs of Points
Network Optimization on Partitioned Pairs of Points Esther M. Arkin1, Aritra Banik2, Paz Carmi2, Gui Citovsky3, Su Jia1, Matthew J. Katz2, Tyler Mayer1, and Joseph S. B. Mitchell1 1Dept. of Applied Mathematics and Statistics, Stony Brook University, Stony Brook USA., esther.arkin, su.jia, tyler.mayer, joseph.mitchellf @stonybrook.edu 2Dept. of Computer Science, Ben-Guriong University, Beersheba Israel., aritrabanik,carmip @gmail.com, [email protected] f3Google, Manhattan USA.,g [email protected] Abstract Given n pairs of points, = p1; q1 ; p2; q2 ;:::; pn; qn , in some metric space, we studyS the problemff g off two-coloringg f the pointsgg within each pair, red and blue, to optimize the cost of a pair of node- disjoint networks, one over the red points and one over the blue points. In this paper we consider our network structures to be spanning trees, traveling salesman tours or matchings. We consider several different weight functions computed over the network structures induced, as well as several different objective functions. We show that some of these problems are NP-hard, and provide constant factor approximation al- gorithms in all cases. arXiv:1710.00876v1 [cs.CG] 2 Oct 2017 1 Introduction We study a class of network optimization problems on pairs of sites in a metric space. Our goal is to determine how to split each pair, into a \red" site and a \blue" site, in order to optimize both a network on the red sites and a network on the blue sites. In more detail, given n pairs of points, = p1; q1 ; p2; q2 ;:::; pn; qn , in the Euclidean plane or in a general S ff g f g f gg Sn metric space, we define a feasible coloring of the points in S = pi; qi i=1f g to be a coloring, S = R B, such that pi R if and only if qi B.