Stochastic Gradient versus Recursive Least Squares Learning
In this paper, we perform an in—depth investigation of relative merits of two adaptive learning algorithms with constant gain, Recursive Least Squares (RLS) and Stochastic Gradient (SG), using the Phelps model of monetary policy as a testing ground. The behavior of the two learning algorithms is very different. Under the mean (averaged) RLS dynamics, the Self—Confirming Equilibrium (SCE) is stable for initial conditions in a very small region around the SCE. Large distance movements of perceived model parameters from their SCE values, or “escapes”, are observed. On the other hand, the SCE is stable under the SG mean dynamics in a large region. However, actual behavior of the SG learning algorithm is divergent for a wide range of constant gain parameters, including those that could be justified as economically meaningful. We explain the discrepancy by looking into the structure of eigenvalues and eigenvectors of the mean dynamics map under SG learning. Results of our paper hint that caution is needed when constant gain learning algorithms are used. If the mean dynamics map is stable but not contracting in every direction, and most eigenvalues of the map are close to the unit circle, the constant gain learning algorithm might diverge.
|Date of creation:||Oct 2006|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (+420) 224 005 123
Fax: (+420) 224 005 333
Web page: http://www.cerge-ei.cz
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- In-Koo Cho & Noah Williams & Thomas J. Sargent, 2002.
"Escaping Nash Inflation,"
Review of Economic Studies,
Oxford University Press, vol. 69(1), pages 1-40.
- Dmitri Kolyuzhnov & Anna Bogomolova & Sergey Slobodyan, 2006.
"Escape Dynamics: A Continuous—Time Approximation,"
CERGE-EI Working Papers
wp285, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
- Thomas Sargent & Noah Williams & Tao Zha, 2006.
"The Conquest of South American Inflation,"
NBER Working Papers
12606, National Bureau of Economic Research, Inc.
- Seppo Honkapohja & Kaushik Mitra, 2006.
"Learning Stability in Economies with Heterogeneous Agents,"
Review of Economic Dynamics,
Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 284-309, April.
- Honkapohja, Seppo & Mitra, Kaushik, 2002. "Learning stability in economics with heterogeneous agents," Working Paper Series 0120, European Central Bank.
- Kaushik Mitra & Seppo Honkapohja, 2004. "Learning Stability in Economies with Heterogenous Agents," Royal Holloway, University of London: Discussion Papers in Economics 04/17, Department of Economics, Royal Holloway University of London, revised Jul 2004.
- Seppo Honkapohja & Kaushik Mitra, 2002. "Learning Stability in Economies with Heterogenous Agents," CESifo Working Paper Series 772, CESifo Group Munich.
- Chryssi Giannitsarou, 2003. "Heterogeneous Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 885-906, October.
- Evans, G.W. & Honkapohja ,S. & Williams, N., 2005.
"Generalized Stochastic Gradient Learning,"
Cambridge Working Papers in Economics
0545, Faculty of Economics, University of Cambridge.
- George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," NBER Technical Working Papers 0317, National Bureau of Economic Research, Inc.
- George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," University of Oregon Economics Department Working Papers 2005-17, University of Oregon Economics Department, revised 18 May 2008.
- George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," CESifo Working Paper Series 1576, CESifo Group Munich.
- William Poole & Robert H. Rasche, 2002.
Federal Reserve Bank of St. Louis, issue Nov, pages 1-6.
When requesting a correction, please mention this item's handle: RePEc:cer:papers:wp309. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jana Koudelkova)
If references are entirely missing, you can add them using this form.