Abstract
The difficulty of selecting a good step size sequence {ε n } has been a serious handicap in applications. In a fundamental paper, Polyak and Juditsky [142] showed that (loosely speaking) if ε n goes to zero slower than O(1/n), the averaged sequence \( \sum\nolimits_{i = 1}^n {{\theta _i}/n} {\text{ }} \) converges to its limit at an optimum rate.
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© 1997 Springer Science+Business Media New York
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Kushner, H.J., Yin, G.G. (1997). Averaging of the Iterates. In: Stochastic Approximation Algorithms and Applications. Applications of Mathematics, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-2696-8_11
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DOI: https://doi.org/10.1007/978-1-4899-2696-8_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4899-2698-2
Online ISBN: 978-1-4899-2696-8
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