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Stochastic Gradient Learning And Instability: An Example

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  • Slobodyan, Sergey
  • Bogomolova, Anna
  • Kolyuzhnov, Dmitri

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.

Suggested Citation

  • Slobodyan, Sergey & Bogomolova, Anna & Kolyuzhnov, Dmitri, 2016. "Stochastic Gradient Learning And Instability: An Example," Macroeconomic Dynamics, Cambridge University Press, vol. 20(3), pages 777-790, April.
    • Handle: RePEc:cup:macdyn:v:20:y:2016:i:03:p:777-790_00
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    Cited by:

    1. Audzei, Volha & Slobodyan, Sergey, 2022. "Sparse restricted perceptions equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).

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