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.
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- Thomas Sargent & Noah Williams & Tao Zha, 2009.
"The Conquest of South American Inflation,"
Journal of Political Economy,
University of Chicago Press, vol. 117(2), pages 211-256, 04.
- Thomas Sargent & Noah Williams & Tao Zha, 2006. "The conquest of South American inflation," FRB Atlanta Working Paper No. 2006-20, Federal Reserve Bank of Atlanta.
- Thomas Sargent & Noah Williams & Tao Zha, 2006. "The Conquest of South American Inflation," NBER Working Papers 12606, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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, 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.
- Seppo Honkapohja & Kaushik Mitra, 2002. "Learning Stability in Economies with Heterogenous Agents," CESifo Working Paper Series 772, CESifo Group Munich.
- Honkapohja, Seppo & Mitra, Kaushik, 2002. "Learning stability in economics with heterogeneous agents," Working Paper Series 0120, European Central Bank.
- 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.
- Cho, In-Koo & Williams, Noah & Sargent, Thomas J, 2002.
"Escaping Nash Inflation,"
Review of Economic Studies,
Wiley Blackwell, vol. 69(1), pages 1-40, January.
- Chryssi Giannitsarou, 2003. "Heterogeneous Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 885-906, October.
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