On the Lock-in Probability of Stochastic Approximation

  • Authors:
  • V. S. Borkar

  • Affiliations:
  • School of Technology and Computer Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India (e-mail: borkar@tifr.res.in)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2002

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Abstract

For a stochastic approximation-type recursion with finitely many possible limit points, we find a lower bound on the probability of converging to a prescribed point in its ‘domain of attraction’. This has implications for the lock-in phenomena in the stochastic models of increasing return economics and the sample complexity of stochastic approximation algorithms in engineering.