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Stochastic Gradient versus Recursive Least Squares Learning

  • Sergey Slobodyan
  • Anna Bogomolova
  • Dmitri Kolyuzhnov

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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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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  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 & Williams, Noah & Sargent, Thomas J, 2002. "Escaping Nash Inflation," Review of Economic Studies, Wiley Blackwell, vol. 69(1), pages 1-40, January.
  3. 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.
  4. Chryssi Giannitsarou, 2003. "Heterogeneous Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 885-906, October.
  5. William Poole & Robert H. Rasche, 2002. "Flation," Review, Federal Reserve Bank of St. Louis, issue Nov, pages 1-6.
    • William Poole, 2002. "Flation," Speech 49, Federal Reserve Bank of St. Louis.
  6. Kolyuzhnov, Dmitri & Bogomolova, Anna & Slobodyan, Sergey, 2014. "Escape dynamics: A continuous-time approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 161-183.
  7. George W. Evans & Seppo Honkapohja & Noah Williams, 2010. "Generalized Stochastic Gradient Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 237-262, 02.
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