Stochastic gradient learning and instability: an example

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11640%2F16%3A00459193" target="_blank" >RIV/00216208:11640/16:00459193 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S1365100514000583" target="_blank" >http://dx.doi.org/10.1017/S1365100514000583</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S1365100514000583" target="_blank" >10.1017/S1365100514000583</a>

Result language
angličtina
Original language name
Stochastic gradient learning and instability: an example
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
AH - Economics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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