On Decentralized Estimation With Active Queries

We consider the problem of decentralized 20 questions with noise for multiple players/agents under the minimum entropy criterion in the setting of stochastic search over a parameter space, with application to target localization. We propose decentralized extensions of the active query-based stochastic search strategy that combines elements from the 20 questions approach and social learning. We prove convergence to correct consensus on the value of the parameter. This framework provides a flexible and tractable mathematical model for decentralized parameter estimation systems based on active querying. We illustrate the effectiveness and robustness of the proposed decentralized collaborative 20 questions algorithm for random network topologies with information sharing.

[1]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

[2]  Anand D. Sarwate,et al.  Broadcast Gossip Algorithms for Consensus , 2009, IEEE Transactions on Signal Processing.

[3]  Ali Jadbabaie,et al.  Non-Bayesian Social Learning , 2011, Games Econ. Behav..

[4]  R. Durrett.  Probability: Theory and Examples , 1993 .

[5]  A. Robert Calderbank,et al.  Toward Resource-Optimal Consensus Over the Wireless Medium , 2012, IEEE Journal of Selected Topics in Signal Processing.

[6]  Alexandros G. Dimakis,et al.  Order-Optimal Consensus Through Randomized Path Averaging , 2010, IEEE Transactions on Information Theory.

[7]  Peter I. Frazier,et al.  Twenty Questions with Noise: Bayes Optimal Policies for Entropy Loss , 2012, Journal of Applied Probability.

[8]  E. Seneta.  Non-negative Matrices and Markov Chains , 2008 .

[9]  Peter I. Frazier,et al.  Bisection Search with Noisy Responses , 2013, SIAM J. Control. Optim..

[10]  Keith D. Kastella,et al.  Foundations and Applications of Sensor Management , 2010 .

[11]  Ilse C. F. Ipsen,et al.  Ergodicity Coefficients Defined by Vector Norms , 2011, SIAM J. Matrix Anal. Appl..

[12]  Donald Geman,et al.  An Active Testing Model for Tracking Roads in Satellite Images , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Robert Nowak,et al.  Active Learning and Sampling , 2008 .

[14]  M. Degroot.  Reaching a Consensus , 1974 .

[15]  Stephen P. Boyd,et al.  Randomized gossip algorithms , 2006, IEEE Transactions on Information Theory.

[16]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[17]  Soummya Kar,et al.  Gossip Algorithms for Distributed Signal Processing , 2010, Proceedings of the IEEE.

[18]  John N. Tsitsiklis,et al.  Problems in decentralized decision making and computation , 1984 .

[19]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[20]  George Cybenko,et al.  Dynamic Load Balancing for Distributed Memory Multiprocessors , 1989, J. Parallel Distributed Comput..

[21]  Soummya Kar,et al.  Convergence Rate Analysis of Distributed Gossip (Linear Parameter) Estimation: Fundamental Limits and Tradeoffs , 2010, IEEE Journal of Selected Topics in Signal Processing.

[22]  Minghua Chen,et al.  Markov Approximation for Combinatorial Network Optimization , 2013, IEEE Transactions on Information Theory.

[23]  J. Norris.  Appendix: probability and measure , 1997 .

[24]  Raphael Sznitman,et al.  Active Testing for Face Detection and Localization , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[26]  Alfred O. Hero,et al.  Collaborative 20 Questions for Target Localization , 2013, IEEE Transactions on Information Theory.