Discrete Parameter Optimization

In this chapter, we consider the case when optimization has to be performed over a parameter set that is discrete valued and has a finite number of points. We present adaptations of the SPSA and SF algorithms discussed previously using certain projection mappings. We consider here the case of a long-run average cost objective.

[1]  L. Gerencsér,et al.  Stochastic approximation on discrete sets using simultaneous difference approximations , 2004, Proceedings of the 2004 American Control Conference.

[2]  Michel Loève,et al.  Probability Theory I , 1977 .

[3]  Shalabh Bhatnagar,et al.  Stochastic Algorithms for Discrete Parameter Simulation Optimization , 2011, IEEE Transactions on Automation Science and Engineering.

[4]  Yu-Chi Ho,et al.  Ordinal optimization of DEDS , 1992, Discret. Event Dyn. Syst..

[5]  Chun-Hung Chen,et al.  Simulation Budget Allocation for Further Enhancing the Efficiency of Ordinal Optimization , 2000, Discret. Event Dyn. Syst..

[6]  C. Dunnett A Multiple Comparison Procedure for Comparing Several Treatments with a Control , 1955 .

[7]  Discrete simultaneous perturbation stochastic approximation on loss function with noisy measurements , 2011, Proceedings of the 2011 American Control Conference.

[8]  Shalabh Bhatnagar,et al.  A Discrete Parameter Stochastic Approximation Algorithm for Simulation Optimization , 2005, Simul..

[9]  László Gerencsér,et al.  Convergence rate of moments in stochastic approximation with simultaneous perturbation gradient approximation and resetting , 1999, IEEE Trans. Autom. Control..

[10]  R. Bechhofer A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances , 1954 .

[11]  C. Cassandras,et al.  Generalized Surrogate Problem Methodology for Online Stochastic Discrete Optimization , 2002 .

[12]  Shalabh Bhatnagar,et al.  Optimal Threshold Policies for Admission Control in Communication Networks via Discrete Parameter Stochastic Approximation , 2005, Telecommun. Syst..

[13]  Jürgen Branke,et al.  Selecting a Selection Procedure , 2007, Manag. Sci..

[14]  P. Schweitzer Perturbation theory and finite Markov chains , 1968 .

[15]  Barry L. Nelson,et al.  Ranking and Selection for Steady-State Simulation: Procedures and Perspectives , 2002, INFORMS J. Comput..

[16]  V. Borkar Probability Theory: An Advanced Course , 1995 .

[17]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.