Necessary and sufficient conditions for convergence of stochastic approximation algorithms under arbitrary disturbances

Sanjeev R. Kulkarni, Charlie S. Horn

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations

Abstract

A parametrized extension of the Kushner-Clark condition is introduced for the study of convergence of stochastic approximation algorithms. Our results provide necessary and sufficient conditions for convergence that hold in a Hilbert space setting and apply to general gain sequences. These results exhibit the interplay among the noise sequence, the gain sequence, and key properties of the underlying function. The proof is direct, completely deterministic, and is elementary, involving only basic notions of convergence. Some corollaries to our main result are also presented.

Original languageEnglish (US)
Pages (from-to)3843-3848
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume4
StatePublished - Dec 1 1995
EventProceedings of the 1995 34th IEEE Conference on Decision and Control. Part 1 (of 4) - New Orleans, LA, USA
Duration: Dec 13 1995Dec 15 1995

All Science Journal Classification (ASJC) codes

  • Chemical Health and Safety
  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality

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