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1998-1999 | 25 | 3 | 339-358
Tytuł artykułu

Bayesian parameter estimation and adaptive control of Markov processes with time-averaged cost

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper considers Bayesian parameter estimation and an associated adaptive control scheme for controlled Markov chains and diffusions with time-averaged cost. Asymptotic behaviour of the posterior law of the parameter given the observed trajectory is analyzed. This analysis suggests a "cost-biased" estimation scheme and associated self-tuning adaptive control. This is shown to be asymptotically optimal in the almost sure sense.
Rocznik
Tom
25
Numer
3
Strony
339-358
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-08-20
poprawiono
1998-01-06
Twórcy
autor
  • Department of Computer Science and Automation Indian Institute of Science Bangalore 560012, India
  • OA Division (SW Team) Samsung Electronics Co. Ltd. Suwon, P.O.B. 105, Kyungki-Do South Korea 440600
Bibliografia
  • [1] R. Agrawal, D. Teneketzis and V. Anantharam, Asymptotically efficient adaptive allocation schemes for controlled Markov chains: finite parameter space, IEEE Trans. Automatic Control AC-34 (1989), 1249-1259.
  • [2] A. Barron, Are Bayes rules consistent in information?, in: Problems in Communication and Computation, T. M. Cover and B. Gopinath (eds.), Springer, New York, 1987, 85-91.
  • [3] R. N. Bhattacharya, Asymptotic behaviour of several dimensional diffusions, in: Stochastic Nonlinear Systems, L. Arnold and R. Lefever (eds.), Springer, New York, 1981, 86-91.
  • [4] D. Blackwell and L. Dubins, Merging of opinions with increasing information, Ann. Math. Statist. 33 (1962), 882-887.
  • [5] V. S. Borkar, Control of Markov chains with long run average cost criterion, in: Stochastic Differential Systems, Stochastic Control Theory and Applications, W. H. Fleming and P. L. Lions (eds.), Springer, New York, 1987, 57-77.
  • [6] V. S. Borkar, The Kumar-Becker-Lin scheme revisited, J. Optim. Theory Appl. 66 (1990), 289-309.
  • [7] V. S. Borkar, Self-tuning control of diffusions without the identifiability condition, ibid. 68 (1991), 117-137.
  • [8] V. S. Borkar, On the Milito-Cruz adaptive control scheme for Markov chains, ibid. 77 (1993), 387-397.
  • [9] V. S. Borkar, A modified self-tuner for controlled diffusions with an unknown parameter, in: Mathematical Theory of Control (Bombay, 1990), A. V. Balakrishnan and M. C. Joshi (eds.), Marcel Dekker, 1992, 57-67.
  • [10] V. S. Borkar and M. K. Ghosh, Ergodic and adaptive control of nearest neighbour motions, Math. Control Signals and Systems 4 (1991), 81-98.
  • [11] V. S. Borkar and M. K. Ghosh, Ergodic control of multidimensional diffusions II: adaptive control, Appl. Math. Optim. 21 (1990), 191-220.
  • [12] V. S. Borkar and P. P. Varaiya, Identification and adaptive control of Markov chains I: finite parameter case, IEEE Trans. Automatic Control 24 (1979), 953-957.
  • [13] V. S. Borkar and P. P. Varaiya, Identification and adaptive control of Markov chains, SIAM J. Control Optim. 20 (1982), 470-488.
  • [14] E. K. P. Chong and P. J. Ramadge, Stochastic optimization of regenerative systems using infinitesimal perturbation analysis, IEEE Trans. Automatic Control 39 (1994), 1400-1410.
  • [15] Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, Springer, New York, 1979.
  • [16] G. B. Di Masi and Ł. Stettner, Bayesian ergodic adaptive control of discrete time Markov processes, Stochastics Stochastic Reports 54 (1995), 301-316.
  • [17] B. Doshi and S. E. Shreve, Randomized self-tuning control of Markov chains, J. Appl. Probab. 17 (1980), 726-734.
  • [18] B. Hajek, Hitting-time and occupation-time bounds implied by drift analysis with applications, Adv. Appl. Probab. 14 (1982), 502-525.
  • [19] P. R. Kumar and A. Becker, A new family of optimal adaptive controllers for Markov chains, IEEE Trans. Automatic Control 27 (1982), 137-142.
  • [20] P. R. Kumar and W. Lin, Optimal adaptive controllers for Markov chains, ibid. 27 (1982), 756-774.
  • [21] P. R. Kumar and P. P. Varaiya, Stochastic Systems--Estimation, Identification and Adaptive Control, Prentice-Hall, 1986.
  • [22] P. Mandl, Estimation and control in Markov chains, Adv. Appl. Probab. 6 (1974), 40-60.
  • [23] R. Milito and J. B. Cruz, Jr., An optimization oriented approach to adaptive control of Markov chains, IEEE Trans. Automatic Control 32 (1987), 754-762.
  • [24] J. N. Tsitsiklis, Asynchronous stochastic approaximation and Q-learning, Machine Learning 16 (1994), 195-202.
  • [25] K. Van Hee, Bayesian Control of Markov Chains, Math. Center Tracts, 95, Math. Center, Amsterdam, 1978.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv25i3p339bwm
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