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Stochastic Gradient versus Recursive Least Squares Learning

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  • Sergey Slobodyan
  • Anna Bogomolova
  • Dmitri Kolyuzhnov

Abstract

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. RLS is characterized by a very small region of attraction of the Self—Confirming Equilibrium (SCE) under the mean, or averaged, dynamics, and “escapesâ€, 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.

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File URL: http://repec.org/sce2006/up.28420.1141162925.pdf
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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 446.

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Date of creation: 04 Jul 2006
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Handle: RePEc:sce:scecfa:446

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Keywords: constant gain adaptive learning; E—stability; recursive least squares; stochastic gradient learning;

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  1. 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.
  2. Cho, In-Koo & Sargent, Thomas J., 2000. "Escaping Nash inflation," Working Paper Series 0023, European Central Bank.
  3. 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.
  4. 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.
  5. Thomas Sargent & Noah Williams & Tao Zha, 2006. "The conquest of South American inflation," Working Paper 2006-20, Federal Reserve Bank of Atlanta.
  6. William Poole, 2002. "Flation," Speech 49, Federal Reserve Bank of St. Louis.
  7. 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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Cited by:
  1. George W. Evans & Seppo Honkapohja, 2009. "Robust Learning Stability with Operational Monetary Policy Rules," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.), Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 5, pages 145-170 Central Bank of Chile.

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