Stochastic Gradient versus Recursive Least Squares Learning
AbstractIn 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.
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 446.
Date of creation: 04 Jul 2006
Date of revision:
constant gain adaptive learning; Eâ€”stability; recursive least squares; stochastic gradient learning;
Other versions of this item:
- Sergey Slobodyan & Anna Bogomolova, & Dmitri Kolyuzhnov, 2006. "Stochastic Gradient versus Recursive Least Squares Learning," CERGE-EI Working Papers wp309, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
- E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
- E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-07-15 (All new papers)
- NEP-EVO-2006-07-15 (Evolutionary Economics)
- NEP-MAC-2006-07-15 (Macroeconomics)
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