Stochastic Optimization with Partial Information
This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: ARISTEIA II. Investing in knowledge society through the European Social Fund.
Project Title
Optimization of stochastic systems under partial information and applications.
Project Duration
1 year (November 2014-October 2015)
Keywords
Stochastic Optimization, Partial Information, Queueing Theory, Game Theory, Markov Decision Processes.
Summary
The goal of this research project is to develop innovative mathematical models for control of stochastic systems
under partial information. Under this general framework, the research focuses on the following specific objectives,
in which the common thread is the notion of incomplete information and adaptive optimization:
- adaptive control of stochastic systems with constraints,
- models of learning in games, and
- strategic queueing and the price of anarchy under incomplete information.
The problems that are studied have wide applicability, ranging from production and supply chain management, design
and control of service systems, resource allocation under incomplete information, etc. The methodologies that are used
come from a variety of areas, namely Stochastic Operations Research and in particular Markov Decision Processes, Inventory Theory and Queueing Theory, Game Theory, and Probability and Statistics. The research project aspires to promote interdisciplinary
collaboration in the area of Stochastic Optimization, by forming a research group whose members are faculty in Mathematics and Engineering in two universities.
Research Group
- Principal Inverstigator
- Senior Investigators
- Economou, Antonis, Associate Professor, Department of Mathematics, University of Athens.
- Liberopoulos, George, Professor, Department of Mechanical Engineering, University of Thessaly.
- Melolidakis, Costis, Associate Professor, Department of Mathematics, University of Athens.
- Pandelis, Dimitrios, Assistant Professor, Department of Mechanical Engineering, University of Thessaly.
- Papadatos, Nikolaos, Associate Professor, Department of Mathematics, University of Athens.
- Junior Investigators
- Leonardos, Stefanos, PhD Student, Department of Mathematics, University of Athens.
- Stergiou, Iliana, MSc Student, Department of Mathematics, University of Athens.
- Vasiliadis, George, PostDoc Researcher.
- Technical Staff
Publications (Papers)
Conference presentations (Slides)
Bibliography (References)
- Books
- Hassin, R. and Haviv, M. (2003) To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Kluwer Academic Publishers, Boston.
- Stidham, S. Jr. (2009) Optimal Design of Queueing Systems. CRC Press.
- Papers in journals
- Burnetas, A. and Economou, A. (2007) Equilibrium customer strategies in a single
server Markovian queue with setup times.
Queueing Systems 56, 213-228.
- Economou, A. and Kanta, S. (2008) Optimal balking strategies and pricing for the single
server Markovian queue with compartmented waiting space.
Queueing Systems 59, 237-269.
DOI: 10.1007/s11134-008-9083-8
- Economou, A. and Kanta, S. (2008) Equilibrium balking strategies in the observable single
server queue with breakdowns and repairs.
Operations Research Letters 36, 696-699.
DOI: 10.1016/j.orl.2008.06.006
- Economou, A. and Kapodistria, S. (2009) q-series in Markov chains with binomial transitions:
Studying a queue with synchornization.
Probability in the Engineering and Informational Sciences 23, 75-99.
DOI: 10.1017/S0269964809000084
- Economou, A. and Kanta, S. (2011) Equilibrium customer strategies and social-profit
maximization in the single-server constant retrial queue.
Naval Research Logistics 58, 107-122.
DOI: 10.1002/nav.20444
- Economou, A., Gomez-Corral, A. and Kanta, S. (2011) Optimal balking strategies in single-server
queues with general service and vacation times.
Performance Evaluation 68, 967-982.
DOI: 10.1016/j.peva.2011.07.001
- Economou, A. and Manou, A. (2012) Equilibrium balking strategies for a clearing queueing system in
alternating environment.
Annals of Operations Research.
DOI: 10.1007/s10479-011-1025-x
- Boudali, O. and Economou, A. (2012) Optimal and equilibrium balking strategies in the single server
Markovian queue with catastrophes.
European Journal of Operational Research 218, 708-715.
DOI: 10.1016/j.ejor.2011.11.043
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Games and Economic Behavior 8,6-19.
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- Aumann, R. and Dreze, J. (2008) Rational expectations in games,
The American Economic Review 98, 72-86.
- Barelli, P. (2009)., Consistency of beliefs and epistemic conditions for Nash and correlated equilibria,
Games and Economic Behavior 67 , 363–375.
- Bertsekas, D. and Tsitsiklis, J. (1996)
Neuro-dynamic Programming,, Athena Scientific, Belmont, MA.
- Burnetas, A. and Katehakis M. (1996) Optimal Adaptive Policies for Sequential Allocation Problems.
Advances in Applied Mathematics 17, 122-142.
- Burnetas, A. N. and Katehakis, M. N. (1997) Optimal Adaptive Policies for Markov Decision Processes.
Mathematics of Operations Research, 22 , 222-255.
- Burnetas, A.N. and Kanavetas, O. (2012) Adaptive Policies for Sequential Sampling under Incomplete Information and a Cost Constraint.
Applications of Mathematics in Military Science , Daras, N. and Pardalos, P. (eds), Springer, Ch. 8, in press.
- Durieu, J., Solal, P. and Tercieux, O. (2011) Adaptive learning and p-best response sets,
Intern. Journal of Game Theory (to appear)—published on line.
- Fudenberg, D. and Levine, D. (1998)
The Theory of Learning in Games (Economic Learning and Social Evolution), The MIT Press, Boston.
- Fudenberg, D. and Tirole, J.
Game Theory, MIT Press, Cambridge, MA.
- Gittins, J. (1989)
Multi-armed Bandit Allocation Indices. Wiley, Chichester, NY.
- Golman, R. (2011) Why learning doesn’t add up: equilibrium selection with a composition of learning rules,
, Intern. Journal of Game Theory 40, 719-733.
- Guo, P. and Zipkin, P. (2007) Analysis and comparison of queues with different levels of delay information.
Management Science 53, 962-970.
- Hassin, R. and Haviv, M. (1997) Equilibrium threshold strategies: the case of queues with priorities.
Operations Research 45 , 966-973.
- Hernandez-Lerma, O. (1989)
Adaptive Markov Control Processes. Springer, NY.
- Kerner, Y. (2011) Equilibrium joining probabilities for an M/G/1 queue.
Games and Economic Behavior 71 , 521-526.
- Kreps, D. and Wilson, R (1982), Sequential equilibria,
Econometrica 50 , 863-894.
- Kushner, H. and Yin, G. (1997)
Stochastic Approximation Algorithms and Applications. Springer, NY.
- Lai, T. and Robbins, H. (1985) Asymptotically Efficient Adaptive Allocation Rules.
Advances in Applied Mathematics 6 , 4-22.
- Latouche, G. and Ramaswami, V. (1999)
Introduction to Matrix Analytic Methods in Stochastic Modeling. SIAM-ASA.
- Maitra, A. and Sudderth, W. (1996)
Discrete Gambling and Stochastic Games, Springer, NY.
- Smith, J.M. and Price, G. (1973), The Logic of Animal Conflict.
Nature 246 , 15-18.
- Smith, J.M. (1982)
Evolution and the Theory of Games. Cambridge University Press.
- Monderer, D. and Shapley, L. (1996a) Potential Games.
Games and Economic Behavior. 14 , 124–143.
- Monderer, D. and Shapley, L. (1996b) Fictitious Play Property for Games with Identical Interests.
Journal of Economic Theory 68 , 258-265.
- Naor, P. (1969) The regulation of queues by levying tolls.
Econometrica 37 , 15-24.
- Poznyak, A., Najim, K. and Ramirez, E. (2000)
Self-Learning Control of Finite Markov Chains, CRC.
- Liu, Q. (2010) Higher-Order Beliefs and Epistemic Conditions for Nash Equilibrium, preprint, Dept. of Economics, University of Pennsylvania
- Robbins, H. and Monro, S. (1951) A Stochastic Approximation Method.
Annals of Mathematical Statistics 22 , 400-407.
- Robbins, H. (1952) Some Aspects of the Sequential Design of Experiments.
Bulletin of the American Mathematical Society. 58 , 527-535.
- Samuelson, L. (1998)
Evolutionary Games and Equilibrium Selection (Economic Learning and Social Evolution). The MIT Press, Boston.
- Papers in conference proceedings
Last revision: September 10, 2015