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Using Randomization to Break the Curse of Dimensionality

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  • John Rust

Abstract

This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems. The author proves that these algorithms succeed in breaking the 'curse of dimensionality' for a subclass of Markovian decision problems known as discrete decision processes.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 65 (1997)
Issue (Month): 3 (May)
Pages: 487-516

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Handle: RePEc:ecm:emetrp:v:65:y:1997:i:3:p:487-516

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  1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
  2. 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.
  3. Lars Peter Hansen & Ellen R. McGrattan & Thomas J. Sargent, 1994. "Mechanics of forming and estimating dynamic linear economies," Staff Report 182, Federal Reserve Bank of Minneapolis.
  4. 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.
  5. 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.
  6. 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.
  7. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1, January.
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