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Generalized Stochastic Gradient Learning

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  • George W. Evans
  • Seppo Honkapohja
  • Noah Williams

Abstract

We study the properties of generalized stochastic gradient (GSG) learning in forward-looking models. We examine how the conditions for stability of standard stochastic gradient (SG) learning both differ from and are related to E-stability, which governs stability under least squares learning. SG algorithms are sensitive to units of measurement and we show that there is a transformation of variables for which E-stability governs SG stability. GSG algorithms with constant gain have a deeper justification in terms of parameter drift, robustness and risk sensitivity.

Suggested Citation

  • George W. Evans & Seppo Honkapohja & Noah Williams, 2005. "Generalized Stochastic Gradient Learning," NBER Technical Working Papers 0317, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0317 Note: TWP
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    References listed on IDEAS

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    1. George W. Evans & Seppo Honkapohja, 2003. "Expectations and the Stability Problem for Optimal Monetary Policies," Review of Economic Studies, Oxford University Press, vol. 70(4), pages 807-824.
    2. Evans, George W. & Honkapohja, S., 1998. "Stochastic gradient learning in the cobweb model," Economics Letters, Elsevier, vol. 61(3), pages 333-337, December.
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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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