Abstract
As shown in Chapter 2, performance derivatives for Markov systems depend heavily on performance potentials. In this chapter, we first discuss the numerical methods and sample-path-based algorithms for estimating performance potentials, and we then derive the sample-path-based algorithms for estimating performance derivatives. In performance optimization, the process of estimating the potentials and performance derivatives from a sample path is called learning.
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References
P. Bratley, B. L. Fox, and L. E. Schrage, A Guide to Simulation, Second Edition, Springer-Verlag, New York, 1987.
P. Bremaud, “Maximal Coupling and Rare Perturbation Sensitivity Analysis,” Queueing Systems: Theory and Applications, Vol. 11, 307-333, 1992.
L. Dai, “Rate of Convergence for Derivative Estimation of Discrete-Time Markov Chains Via Finite-Difference Approximations with Common Random Numbers,” SIAM Journal on Applied Mathematics, Vol. 57, 731-751, 1997.
L. Dai, “Perturbation Analysis via Coupling,” IEEE Transactions on Automatic Control, Vol. 45, 614-628, 2000.
P. W. Glynn, “Regenerative Structure of Markov Chains Simulated Via Common Random Numbers,” Operations Research Letters, Vol. 4, 49-53, 1985.
P. Heidelberger and D. L. Iglehart, “Comparing Stochastic Systems Using Regenerative Simulation with Common Random Numbers,” Advances in Applied Probability, Vol. 11, 804-819, 1979.
P. L’Ecuyer, “Convergence Rate for Steady-State Derivative Estimators,” Annals of Operations Research, Vol. 39, 121-136, 1992.
P. L’Ecuyer and G. Perron, “On the Convergence Rates of IPA and FDC Derivative Estimators,” Operations Research, Vol. 42, 643-656, 1994.
G. Pflug, Optimization of Stochastic Models: The Interface between Simulation and Optimization, Kluwer Academic Publishers, Boston, Massachusetts, 1996.
G. Pflug and X. R. Cao, unpublished manuscript.
P. Marbach and T. N. Tsitsiklis, “Simulation-Based Optimization of Markov Reward Processes,” IEEE Transactions on Automatic Control, Vol. 46, 191-209, 2001.
J. Baxter and P. L. Bartlett, “Infinite-Horizon Policy-Gradient Estimation,” Journal of Artificial Intelligence Research, Vol. 15, 319-350, 2001.
J. Baxter, P. L. Bartlett, and L. Weaver, “Experiments with Infinite-Horizon, Policy-Gradient Estimation,” Journal of Artificial Intelligence Research, Vol. 15, 351-381, 2001.
D. P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont, Massachusetts, 1995.
M. Baglietto, F. Davoli, M. Marchese, and M. Mongelli, “Neural Approximation of Open-Loop Feedback Rate Control in Satellite Networks,” IEEE Transactions on Neural Networks, Vol. 16, 1195-1211, 2005.
P. Bremaud, R. P. Malhame, and L. Massoulie, “A Manufacturing System with General Stationary Failure Process: Stability and IPA of Hedging Control Policies,” IEEE Transactions on Automatic Control, Vol. 42, 155-170, 1997.
C. A. Brooks and P. Varaiya, “Using Augmented Infinitesimal Perturbation Analysis for Capacity Planning in Intree ATM Networks,” Discrete Event Dynamic Systems: Theory and Applications, Vol. 7, 377-390, 1997.
C. G. Cassandras, G. Sun, C. G. Panayiotou, and Y. Wardi, “Perturbation Analysis and Control of Two-Class Stochastic Fluid Models for Communication Networks,” IEEE Transactions on Automatic Control, Vol. 48, 770-782, 2003.
F. Davoli, M. Marchese, and M. Mongelli, “Resource Allocation in Satellite Networks: Certainty Equivalent Approaches Versus Sensitivity Estimation Algorithms,” International Journal of Communication Systems, Vol. 18, 3-36, 2005.
Y. C. Ho, M. A. Eyler, and T. T. Chien, “A Gradient Technique for General Buffer Storage Design in A Production Line,” International Journal of Production Research, Vol. 17, 557-580, 1979.
Y. C. Ho, M. A. Eyler, and T. T. Chien, “A New Approach to Determine Parameter Sensitivities of Transfer Lines,” Management Science, Vol. 29, 700-714, 1983.
J. Q. Hu, S. Nananukul, and W. B. Gong, “A New Approach to (s, S) Inventory Systems,” Journal of Applied Probability, Vol. 30, 898-912, 1993.
R. Kapuscinski, and S. Tayur, “A Capacitated Production-inventory Model with Periodic Demand,” Operations Research, Vol. 46, 899-911, 1998.
D. C. Lee, “Applying Perturbation Analysis to Traffic Shaping,” Computer Communications, Vol. 24, 798-810, 2001.
G. Liberopoulos and M. Caramanis, “Infinitesimal Perturbation Analysis for Second Derivative Estimation and Design of Manufacturing Flow Controllers,” Journal of Optimization Theory and Applications, Vol. 81, 297-327, 1994.
G. Liberopoulos and M. Caramanis, “Dynamics and Design of A Class of Parameterized Manufacturing Flow Controllers,” IEEE Transactions on Automatic Control, Vol. 40, 1018-1028, 1995.
N. B. Mandayam and B. Aazhang, “Gradient Estimation for Sensitivity Analysis and Adaptive Multiuser Interference Rejection in Code-Division Multiple-Access Systems,” IEEE Transactions on Communications, Vol. 45, 848-858, 1997.
M. Marchese, A. Garibbo, F. Davoli, and M. Mongelli, “Equivalent Bandwidth Control for the Mapping of Quality of Service in Heterogeneous Networks,” IEEE International Conference on Communications, Vol. 4, 1948-1952, 2004.
M. Marchese and M. Mongelli, “On-Line Bandwidth Control for Quality of Service Mapping over Satellite Independent Service Access Points,” Computer Networks, Vol. 50, 2088-2111, 2006.
N. Miyoshi, “Application of IPA to the Sensitivity Analysis of the Leaky-Bucket Filter with Stationary Gradual Input,” Probability in the Engineering and Informational Sciences, Vol. 14, 219-241, 2000.
C. Panayiotou, C. G. Cassandras, G. Sun, and Y. Wardi, “Control of Communication Networks Using Infinitesimal Perturbation Analysis of Stochastic Fluid Models,” Advances in Communication Control Networks, Lecture Notes in Control and Information Sciences, Vol. 308, 1-26, 2004.
C. Panayiotou and C. G. Cassandras, “Infinitesimal Perturbation Analysis and Optimization for Make-to-Stock Manufacturing Systems Based on Stochastic Fluid Models,” Discrete Event Dynamic Systems: Theory and Applications, Vol. 16, 109-142, 2006.
J. M. Proth, N. Sauer, Y. Wardi, and X. L. Xie, “Marking Optimization of Stochastic Timed Event Graphs Using IPA,” Discrete Event Dynamic Systems: Theory and Applications, Vol. 6, 221-239, 1996.
H. Salehfar and S. Trihadi, “Application of Perturbation Analysis to Sensitivity Computations of Generating Units and System Reliability,” IEEE Transactions on Power Systems, Vol. 13, 152-158, 1998.
U. Savagaonkar, E. K. P. Chong, and R. L. Givan, “Online Pricing for Bandwidth Provisioning in Multi-class Networks,” Computer Networks, Vol. 44, 835-853, 2004.
G. A. Rummery and M. Niranjan, “On-Line Q-Learning Using Connectionist Systems,” Technical Report CUED/F-INFENG/TR 166, Engineering Department, Cambridge University, 1994.
Q. Y. Tang and E. K. Boukas, “Adaptive Control for Manufacturing Systems Using Infinitesimal Perturbation Analysis,” IEEE Transactions on Automatic Control, Vol. 44, 1719-1725, 1999.
A. C. Williams and R. A. Bhandiwad, “A Generating Function Approach to Queueing Network Analysis of Multiprogrammed Computers,” Networks, Vol. 6, 1-22, 1976.
H. Yu, and C. G. Cassandras, “Perturbation Analysis for Production Control and Optimization of Manufacturing Systems,” Automatica, Vol. 40, 945-956, 2004.
H. Yu and C. G. Cassandras, “Perturbation Analysis of Communication Networks with Feedback Control Using Stochastic Hybrid Models,” Nonlinear Analysis - Theory Methods and Applications, Vol. 65, 1251-1280, 2006.
J. G. Kemeny and J. L. Snell, “Potentials for Denumerable Markov Chains,” Journal of Mathematical Analysis and Applications, Vol. 3, 196-260, 1960.
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Cao, XR. (2007). Learning and Optimization with Perturbation Analysis. In: Stochastic Learning and Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-69082-7_3
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