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Multiscale Stochastic Approximation for Parametric Optimization of Hidden Markov Models

Published online by Cambridge University Press:  27 July 2009

Shalabh Bhatnagar  and
Vivek S. Borkar
Shalabh Bhatnagar
Affiliation:
Department of Electrical Engineering, Indian Institute of Science, Bangalore 560 012, India
Vivek S. Borkar
Affiliation:
Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560 012, India
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Abstract

A two–time scale stochastic approximation algorithm is proposed for simulation-based parametric optimization of hidden Markov models, as an alternative to the traditional approaches to “infinitesimal perturbation analysis.” Its convergence is analyzed, and a queueing example is presented.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 4 , October 1997 , pp. 509 - 522
Copyright
Copyright © Cambridge University Press 1997

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References

1.Borkar, V.S. (1990). The Kumar-Becker-Lin scheme revisited. Journal of Optimization Theory and Application 66: 287–309.CrossRefGoogle Scholar
2.Borkar, V.S. (1993). On white noise representations in stochastic realization theory. SIAM Journal on Control and Optimization 31: 1093–1102.CrossRefGoogle Scholar
3.Borkar, V.S. (1995). Probability theory: An advanced course. New York: Springer-Verlag.CrossRefGoogle Scholar
4.Borkar, V.S. & Phansalkar, V.V. (1994). Managing inter processor delays in distributed recursive algorithms. Sadhana 19(6): 995–1003.CrossRefGoogle Scholar
5.Chong, E.K.P. & Ramadge, P.J. (1993). Optimization of queues using an infinitesimal perturbation analysis-based stochastic algorithm with general update times. SIAM Journal on Control and Optimization 31(3): 698–732.CrossRefGoogle Scholar
6.Chong, E.K.P. & Ramadge, P.J. (1994). Stochastic optimization of regenerative systems using infinitesimal perturbation analysis. IEEE Transactions on Automated Control 39(7): 1400–1410.CrossRefGoogle Scholar
7.Dai, L. & Ho, Y.-C. (1995). Structural infinitesimal perturbation analysis (SIPA) for derivative estimation of discrete-event dynamic systems. IEEE Transactions on Automatic Control 40(7): 1154–1166.Google Scholar
8.Gelfand, S.B. & Mitter, S.K. (1992). Recursive stochastic algorithms for global optimization in Rd. SIAM Journal on Control and Optimization 29: 999–1018.CrossRefGoogle Scholar
9.Hirsch, M.W. (1987). Convergent activation dynamics in continuous time networks. Neural Networks 2: 331–349.CrossRefGoogle Scholar
10.Ho, Y.-C. & Cao, X.-R. (1991). Perturbation analysis of discrete event dynamical systems. Boston: Kluwer.CrossRefGoogle Scholar
11.Kushner, H.J. & Clark, D.S. (1978). Stochastic approximation methods for constrained and unconstrained systems. New York: Springer-Verlag.CrossRefGoogle Scholar
12.Kushner, H.J. & Vazquez-Abad, F.J. (1994). Stochastic approximation methods for systems of interest over an infinite horizon. LCDS 94–4: 1–56.Google Scholar
13.Neveu, J. (1975). Discrete parameter martingales. Amsterdam: North-Holland.Google Scholar
14.Parthasarathy, K.R. (1967). Probability on metric spaces. New York: Academic Press.Google Scholar