Stochastic Gradient versus Recursive Least Squares Learning
In this paper we perform an inâ€”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. RLS is characterized by a very small region of attraction of the Selfâ€”Confirming Equilibrium (SCE) under the mean, or averaged, dynamics, and â€œescapesâ€ , or large distance movements of perceived model parameters from their SCE values. 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 the SG learning. As a result of our paper, we express a warning regarding the behavior of constant gain learning algorithm in real time. If many eigenvalues of the mean dynamics map are close to the unit circle, Stochastic Recursive Algorithm which describes the actual dynamics under learning might exhibit divergent behavior despite convergent mean dynamics.
|Date of creation:||04 Jul 2006|
|Date of revision:|
|Contact details of provider:|| Web page: http://comp-econ.org/|
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.:
- Thomas J. Sargent & Noah Williams & Tao Zha, 2006.
"The conquest of South American inflation,"
FRB Atlanta Working Paper
2006-20, Federal Reserve Bank of Atlanta.
- 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 - Economics Institute, Prague.
- William Poole, 2002.
49, Federal Reserve Bank of St. Louis.
- Seppo Honkapohja & Kaushik Mitra, 2002.
"Learning Stability in Economies with Heterogenous Agents,"
CESifo Working Paper Series
772, CESifo Group Munich.
- 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.
- George W. Evans & Seppo Honkapohja & Noah Williams, 2005.
"Generalized Stochastic Gradient Learning,"
CESifo Working Paper Series
1576, CESifo Group Munich.
- 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," NBER Technical Working Papers 0317, National Bureau of Economic Research, Inc.
- Evans, G.W. & Honkapohja ,S. & Williams, N., 2005. "Generalized Stochastic Gradient Learning," Cambridge Working Papers in Economics 0545, Faculty of Economics, University of Cambridge.
- Chryssi Giannitsarou, 2003. "Heterogeneous Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 885-906, October.
- Cho, In-Koo & Sargent, Thomas J., 2000.
"Escaping Nash inflation,"
Working Paper Series
0023, European Central Bank.
When requesting a correction, please mention this item's handle: RePEc:sce:scecfa:446. 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: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.