Abstract
This chapter presents the notions of agreement and common knowledge, and addresses the question of how to achieve common knowledge. It presents a general framework for obtaining solutions to dynamic team problems under decentralized information structures based on dynamic programming and an evolving common knowledge, and applies this primarily in the context of the belief sharing information pattern. Information rates required for tractability of optimal solutions are also presented. Finally, the chapter introduces a team cost-rate function, which provides the minimum cost subject to a rate constraint on the information exchange among members of a team.
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References
Acemoglu, D., Ozdaglar, A.: Opinion dynamics and learning in social networks. Dyn. Games Appl. 1, 3–49 (2010)
Aicardi, M., Davoli, F., Minciardi, R.: Decentralized optimal control of Markov chains with a common past information set. IEEE Trans. Autom. Control 32, 1028–1031 (1987)
Athans, M.: Survey of decentralized control methods. In: 3rd NBER/FRB Workshop on Stochastic Control, Washington D.C, 1974
Aumann, R.J.: Agreeing to disagree. Ann. Stat. 4, 1236–1239 (1976)
Başar, T.: An equilibrium theory for multi-person decision making with multiple probabilistic models. IEEE Trans. Autom. Control 30, 118–132 (1985)
Bamieh, B., Voulgaris, P.: A convex characterization of distributed control problems in spatially invariant systems with communication constraints. Syst. Control Lett. 54, 575–583 (2005)
Barron, A.R.: Information theory and martingales. In: IEEE International Symposium on Information Theory, Recent Results Session, Budapest, Hungary, 1991
Barta, S.M.: On linear control of decentralized stochastic systems. Ph.D. Thesis, Department of EECS, MIT, Cambridge (1978)
Blackwell, D., Dubins, L.: Merging of opinions with increasing information. Ann. Math. Stat. 33, 882–887 (1962)
Borkar, V.S.: Probability Theory: An Advanced Course. Springer, New York (1995)
Borkar, V.S., Varaiya, P.: Asymptotic agreement in distributed estimation. IEEE Trans. Autom. Control 27, 650–655 (1982)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
Brandenburger, A., Dekel, E.: Common knowledge with probability 1. J. Math. Econ. 16, 237–245 (1987)
Burnashev, M.V.: Data transmission over a discrete channel with feedback. Random transmission time. Prob. Inform. Transm. 12, 10–30 (1976)
Castanon, D.A., Teneketzis, D.: Distributed estimation algorithms for nonlinear systems. IEEE Trans. Autom. Control 30, 418–425 (1985)
Castanon, D.A., Teneketzis, D.: Further results on the asymptotic agreement problem. IEEE Trans. Autom. Control 33, 515–523 (1988)
Chong, C.Y., Athans, M.: On the periodic coordination of linear stochastic systems. Automatica 12, 321–335 (1976)
Como, G., Fagnani, F.: Scaling limits for continuous opinion dynamics systems. Ann. Appl. Probab. 21, 1537–1567 (2011)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991)
Csiszar, I., Korner, J.: Information Theory: Coding Theorems for Discrete Memoryless Channels. Akademiai Kiado, Budapest (1981)
Diaconis, P., Freedman, D.: On the consistency of bayes estimates. Ann. Stat. 14, 1–26 (1986)
Fardad, M., Lin, F., Jovanovic, M.R.: Optimal control of vehicular formations with nearest neighbor interactions. IEEE Trans. Autom. Control 57, 2203–2218 (2012)
Foster, D.P., Young, H.P.: On the impossibility of predicting the behavior of rational agents. Proc. Nat.Acad. Sci. 22, 12848–12853 (2001)
Frey, B.J.: Graphical Models for Machine Learning and Digital Communication. MIT Press, Cambridge (1998)
El Gamal, A., Kim, Y.H.: Network Information Theory. Cambridge University Press, Cambridge (2012)
Geanakoplos, J.: Common knowledge. In: Aumann, R.J., Hart, S. (eds.) Handbook of Game Theory, Chapter 40, pp. 1437–1496. Elsevier, Amsterdam (1994)
Geanakoplos, J., Polemarchakis, H.M.: We can’t disagree forever. J. Econ. Theor. 28, 192–200 (1982)
Gharesifard, B., Cortés, J.: Distributed continuous-time convex optimization on weight-balanced digraphs, IEEE Transaction on Automatic Control, to appear (2013)
Giridhar, A., Kumar, P.R.: Toward a theory of in-network computation in wireless sensor networks. IEEE Commun. Mag. 44, 98–107 (2006)
Goldberg, A., Yüksel, S.: On the value of information in decentralized control. Queen’s University Technical Report, August 2012
György, A., Linder, T.: Optimal entropy-constrained scalar quantization of a uniform source. IEEE Trans. Inf. Theor. 46, 2704–2711 (2000)
Huang, M., Caines, P.E., Malhamé, R.P.: Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ε-Nash equilibria. IEEE Trans. Autom. Control 52, 1560–1571 (2007)
Huang, M., Malhamé, R.P., Caines, P.E.: Large population stochastic dynamic games: closed-loop McLean-Vlasov systems and the Nash certainty equivalence principle (Special issue in honour of the 65th birthday of Tyrone Duncan). Commun. Inf. Syst. 6, 221–252 (2006)
Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48, 988–1001 (2003)
Jovanovic, M.R.: On the optimality of localized distributed controllers. Int. J. Syst. Control Commun. 2, 82–99 (2010)
Kalai, E., Lehrer, E.: Weak and strong merging of opinions. J. Math. Econ. 23, 73–100 (1994)
Lasry, J.M., Lions, P.L.: Mean field games. Jpn. J. Math. 2, 229–260 (2007)
Lessard, L., Lall, S.: A state-space solution to the two-player decentralized optimal control problem. In: Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, 2011
Li, S., Başar, T.: Asymptotic agreement and convergence of asynchronous stochastic algorithms. IEEE Trans. Autom. Control 32, 612–618 (1987)
Ma, N., Ishwar, P.: Some results on distributed source coding for interactive function computation. IEEE Trans. Inf. Theor. 57, 6180–6195 (2011)
Mahajan, A.: Sequential decomposition of sequential teams: applications to real-time communication and networked control systems. Ph.D. Dissertation, University of Michigan, Ann Arbor (2008)
Mahajan, A., Martins, N.C., Rotkowitz, M., Yüksel, S.: Information structures in optimal decentralized control. In: IEEE Conference on Decision and Control, Hawaii, USA, 2012
Mahajan, A., Yüksel, S.: Measure and cost dependent properties of information structures. In: Proceedings of the American Control Conference, Baltimore, MD, USA, 2010
Mahmoud, M.S.: Decentralized Systems with Design Constraints. Springer, London (2011)
Mooij, M., Kappen, H.J.: Sufficient conditions for convergence of the sum-product algorithm. IEEE Trans. Inf. Theor. 53, 4422–4437 (2007)
Nachbar, J.H.: Prediction, optimization, and learning in games. Econometrica 65, 275–309 (1997)
Nair, G.N.: A nonstochastic information theory for communication and state estimation. IEEE Trans. Autom. Control (2013, to appear)
Nayyar, A., Mahajan, A., Teneketzis, D.: Decentralized stochastic control with partial sharing information structures: a common information approach. IEEE Transactions on Automatic Control, to appear (2013)
Nayyar, A., Mahajan, A., Teneketzis, D.: Optimal control strategies in delayed sharing information structures. IEEE Trans. Autom. Control 56, 1606–1620 (2011)
Nayyar, A., Mahajan, A., Teneketzis, D.: The common-information approach to decentralized stochastic control. In: Como, G., Bernhardsson, B., Rantzer, A. (eds.) Information and Control in Networks. Springer, New York (2013)
Nedić, A., Özdaglar, A., Parrilo, P.A.: Constrained consensus and optimization in multi-agent networks. IEEE Trans. Autom. Control 55, 922–938 (2010)
Nemirovsky, A.S., Yudin, D.B.: Problem Complexity and Method Efficiency in Optimization. Wiley-Interscience, New York (1983)
Nielsen, L.: Common knowledge, communication and convergence of beliefs. Math. Soc. Sci. 8, 1–14 (1984)
Olshevsky, A.: Efficient information aggregation methods in distributed control and signal processing. Ph.D. Thesis, Department of EECS, MIT, Cambridge, MA (2010)
Ooi, J., Verbout, S., Ludwig, J., Wornell, G.: A separation theorem for periodic sharing information patterns in decentralized control. IEEE Trans. Autom. Control 42, 1546–1550 (1997)
Orlitsky, A., Roche, J.R.: Coding for computing. IEEE Trans. Inf. Theor. 47, 903–917 (2001)
Raginsky, M., Rakhlin, A.: Information-based complexity, feedback and dynamics in convex programming. IEEE Trans. Inf. Theor. 57, 7036– 7056 (2011)
Rotkowitz, M., Lall, S.: A characterization of convex problems in decentralized control. IEEE Trans. Autom. Control 51, 274–286 (2006)
Sabau, S., Martins, N.C.: Stabilizability and norm-optimal control design subject to sparsity constraints. IEEE Trans. Autom. Control, under review (2013)
Singh, M.G.: Decentralised Control. North Holland, Amsterdam (1981)
Srikant, R.: The Mathematics of Internet Congestion Control. Birkhäuser-Springer, USA (2004)
Sundaram, S., Hadjicostis, C.N.: Distributed function calculation and consensus using linear iterative strategies. IEEE J. Sel. Areas Commun.: Issue Control Commun. 26, 650–660 (2008)
Tatikonda, S., Mitter, S.: Control under communication constraints. IEEE Trans. Autom. Control 49(7), 1056–1068 (2004)
Teneketzis, D.: Communication in decentralized control. Ph.D. Dissertation, M.I.T. (1979)
Teneketzis, D., Varaiya, P.: Consensus in distributed estimation. In: Poor, H.V. (ed.) Advances in Statistical Signal Processing, pp. 361–386. JAI Press, Greenwich (1988)
Touri, B., Nedić, A.: On ergodicity, infinite flow and consensus in random models. IEEE Trans. Autom. Control 56, 1593–1605 (2011)
Tsitsiklis, J.N.: Problems in decentralized decision making and computation. Ph.D. Thesis, Department of EECS, MIT, Cambridge, MA (1984)
Tsitsiklis, J.N.: Extremal properties of likelihood-ratio quantizers. IEEE Trans. Commun. 41, 550–558 (1993)
Tsitsiklis, J.N., Athans, M.: Convergence and asymptotic agreement in distributed decision problems. IEEE Trans. Autom. Control 29, 42–50 (1984)
Tsitsiklis, J.N., Athans, M.: On the complexity of decentralized decision making and detection problems. IEEE Trans. Autom. Control 30, 440–446 (1985)
Tsitsiklis, J.N., Luo, Z.-Q.: Communication complexity of convex optimization. J. Complex. 3, 231–243 (1987)
van Zandt, T.: Decentralized Information Processing in the Theory of Organizations, in Contemporary Economic Development Reviewed, vol. 4: The Enterprise and its Environment. Murat Sertel, ed. London: MacMillan. (1997)
Witsenhausen, H.S.: The zero-error side information problem and chromatic numbers. IEEE Trans. Inf. Theor. 22, 592–593 (1976)
Wong, W.S.: Control communication complexity of distributed control systems. SIAM J. Control Optim. 48, 1722–1742 (2009)
Wong, W.S., Baillieul, J.: Control communication complexity of distributed actions. IEEE Trans. Autom. Control. 57, 2731–2345 (2012)
Yao, A.C.C.: Some complexity questions related to distributive computing. In: Proceedings of the of the 11th Annual ACM Symposium on Theory of Computing, 1979
Yoshikawa, T.: Dynamic programming approach to decentralized control problems. IEEE Trans. Autom. Control 20, 796–797 (1975)
Yüksel, S.: Stochastic nestedness and the belief sharing information pattern. IEEE Trans. Autom. Control 54, 2773–2786 (2009)
Yüksel, S., Başar, T.: Minimum rate coding for LTI systems over noiseless channels. IEEE Trans. Autom. Control 51(12), 1878–1887 (2006)
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Yüksel, S., Başar, T. (2013). Agreement in Teams and the Dynamic Programming Approach Under Information Constraints. In: Stochastic Networked Control Systems. Systems & Control: Foundations & Applications. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-7085-4_12
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