### Abstract

We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a sample-path analysis. We prove that the convergence of a stochastic approximation algorithm is equivalent to the convergence of the weighted average of the associated noise sequence. We also present necessary and sufficient noise conditions for convergence of the average of the output of a stochastic approximation algorithm in the linear case. We show that the averaged stochastic approximation algorithms can tolerate a larger class of noise sequences than the stand-alone stochastic approximation algorithms.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Editors | Anon |

Volume | 1 |

State | Published - Dec 1 1996 |

Externally published | Yes |

Event | Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4) - Kobe, Jpn Duration: Dec 11 1996 → Dec 13 1996 |

### Other

Other | Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4) |
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City | Kobe, Jpn |

Period | 12/11/96 → 12/13/96 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*Proceedings of the IEEE Conference on Decision and Control*(Vol. 1)