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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.