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STOCHASTIC GRADIENT LEARNING AND INSTABILITY: AN EXAMPLE

Published online by Cambridge University Press:  28 January 2016

Sergey Slobodyan ,
Anna Bogomolova  and
Dmitri Kolyuzhnov
Sergey Slobodyan*
Affiliation:
CERGE-EI
Anna Bogomolova
Affiliation:
CERGE-EI and Novosibirsk State University
Dmitri Kolyuzhnov
Affiliation:
CERGE-EI and Institute of Economics and Industrial Engineering of the Siberian Branch of the Russian Academy of Sciences
*
Address correspondence to: Sergey Slobodyan, CERGE-EI, a joint workplace of Charles University in Prague and the Economics Institute of the Academy of Sciences of the Czech Republic, Politickych veznu 7, 111 21 Prague, Czech Republic; e-mail: Sergey.Slobodyan@cerge-ei.cz.
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Abstract

In this paper, we investigate real-time behavior of constant-gain stochastic gradient (SG) learning, using the Phelps model of monetary policy as a testing ground. We find that whereas the self-confirming equilibrium is stable under the mean dynamics in a very large region, real-time learning diverges for all but the very smallest gain values. We employ a stochastic Lyapunov function approach to demonstrate that the SG mean dynamics is easily destabilized by the noise associated with real-time learning, because its Jacobian contains stable but very small eigenvalues. We also express caution on usage of perpetual learning algorithms with such small eigenvalues, as the real-time dynamics might diverge from the equilibrium that is stable under the mean dynamics.

Keywords

Constant GainAdaptive LearningE-stabilityStochastic Gradient Learning
Type
Articles
Information
Macroeconomic Dynamics , Volume 20 , Issue 3 , April 2016 , pp. 777 - 790
Copyright
Copyright © Cambridge University Press 2016 

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