A Comparison of Policy Iteration Methods for Solving Continuous-State, Infinite-Horizon Markovian Decision Problems Using Random, Quasi-random, and Deterministic Discretizations
AbstractThis paper compares the performance of the Howard (1960) policy iteration algorithm for infinite-horizon continuous-state Markovian decision processes (MDP's) using alternative random, quasi- random, and deterministic discretizations of the state space, or grids. Each grid corresponds to an embedded finite state MDP whose solution is used to approximate the solution to the original continuous-state Markovian decision process. I extend a result of Rust (1997), to show that policy iteration using random grids succeeds in breaking the curse of dimensionality involved in approximating the solution to a class of continuous-state discrete-action MDP's known as discrete decision processes (DDP's). I compare this ``random policy iteration algorithm'' (RPI) with policy iteration algorithms using deterministically chosen grids including uniform grids and quadrature grids both of which are subject to the curse of dimensionality. I also compare the RPI algorithm to deterministic policy iteration algorithms based on quasi-random or `low discrepancy grids' such as the Sobol' and Tezuka sequences.
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Bibliographic InfoPaper provided by EconWPA in its series Computational Economics with number 9704001.
Length: 50 pages
Date of creation: 21 Apr 1997
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- Michael P. Keane & Kenneth I. Wolpin, 1994.
"The solution and estimation of discrete choice dynamic programming models by simulation and interpolation: Monte Carlo evidence,"
181, Federal Reserve Bank of Minneapolis.
- Keane, Michael P & Wolpin, Kenneth I, 1994. "The Solution and Estimation of Discrete Choice Dynamic Programming Models by Simulation and Interpolation: Monte Carlo Evidence," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 648-72, November.
- Rust, John, 1986. "When Is It Optimal to Kill Off the Market for Used Durable Goods?," Econometrica, Econometric Society, vol. 54(1), pages 65-86, January.
- Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585 Elsevier.
- Lars Peter Hansen & Ellen R. McGrattan & Thomas J. Sargent, 1994.
"Mechanics of forming and estimating dynamic linear economies,"
182, Federal Reserve Bank of Minneapolis.
- Anderson, Evan W. & McGrattan, Ellen R. & Hansen, Lars Peter & Sargent, Thomas J., 1996. "Mechanics of forming and estimating dynamic linear economies," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 4, pages 171-252 Elsevier.
- Rust, John, 1985. "Stationary Equilibrium in a Market for Durable Assets," Econometrica, Econometric Society, vol. 53(4), pages 783-805, July.
- Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
- John Rust, 1997.
"Using Randomization to Break the Curse of Dimensionality,"
Econometric Society, vol. 65(3), pages 487-516, May.
- John Rust & Department of Economics & University of Wisconsin, 1994. "Using Randomization to Break the Curse of Dimensionality," Computational Economics 9403001, EconWPA, revised 04 Jul 1994.
- Tauchen, George, 1990. "Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 49-51, January.
- Ariel Pakes & Paul McGuire, 1997. "Stochastic Algorithms for Dynamic Models: Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Cowles Foundation Discussion Papers 1144, Cowles Foundation for Research in Economics, Yale University.
- Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
- Michael Reiter, 1997.
"Solving higher-dimensional continuous time stochastic control problems by value function regression,"
Economics Working Papers
299, Department of Economics and Business, Universitat Pompeu Fabra, revised Jun 1998.
- Reiter, Michael, 1999. "Solving higher-dimensional continuous-time stochastic control problems by value function regression," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1329-1353, September.
- George J. Hall & John Rust, 1999.
"An Empirical Model of Inventory Investment by Durable Commodity Intermediaries,"
Cowles Foundation Discussion Papers
1228, Cowles Foundation for Research in Economics, Yale University.
- Hall, George & Rust, John, 2000. "An empirical model of inventory investment by durable commodity intermediaries," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 52(1), pages 171-214, June.
- George Hall & John Rust, 1999. "An Empirical Model of Inventory Investment by Durable Commodity Intermediaries," Macroeconomics 9904005, EconWPA.
- Hugo Benitez-Silva, 2000. "A Dynamic Model Of Labor Supply, Consumption/Saving, And Annuity Decisions Under Uncertainty," Computing in Economics and Finance 2000 128, Society for Computational Economics.
- Jacek B. Krawczyk, 2000. "A Markovian Approximated Solution To A Portfolio Management Problem," Computing in Economics and Finance 2000 233, Society for Computational Economics.
- Hugo Benítez-Silva, 2003. "The Annuity Puzzle Revisited," Working Papers wp055, University of Michigan, Michigan Retirement Research Center.
- John Rust & Joseph Traub & Henryk Wozniakowski, 1999. "No Curse of Dimensionality for Contraction Fixed Points Even in the Worst Case," Computational Economics 9902001, EconWPA.
- Ronald Goettler & Ron Shachar, 2000. "Estimating Product Characteristics and Spatial Competition in the Network Television Industry," Econometric Society World Congress 2000 Contributed Papers 1691, Econometric Society.
- Hugo Benitez-Silva, 2000. "A Joint Model of Labor Supply and Consumption Decisions Under Uncertainty," Econometric Society World Congress 2000 Contributed Papers 0196, Econometric Society.
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