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Convergence and convergence rate of stochastic gradient search in the case of multiple and non-isolated extrema

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  • Tadić, Vladislav B.

Abstract

The asymptotic behavior of stochastic gradient algorithms is studied. Relying on results from differential geometry (the Lojasiewicz gradient inequality), the single limit-point convergence of the algorithm iterates is demonstrated and relatively tight bounds on the convergence rate are derived. In sharp contrast to the existing asymptotic results, the new results presented here allow the objective function to have multiple and non-isolated minima. The new results also offer new insights into the asymptotic properties of several classes of recursive algorithms which are routinely used in engineering, statistics, machine learning and operations research.

Suggested Citation

  • Tadić, Vladislav B., 2015. "Convergence and convergence rate of stochastic gradient search in the case of multiple and non-isolated extrema," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1715-1755.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:5:p:1715-1755
    DOI: 10.1016/j.spa.2014.11.001
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    References listed on IDEAS

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    1. Borkar,Vivek S., 2008. "Stochastic Approximation," Cambridge Books, Cambridge University Press, number 9780521515924, September.
    2. Ming Gao Gu & Hong‐Tu Zhu, 2001. "Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 339-355.
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    Cited by:

    1. Prasenjit Karmakar & Shalabh Bhatnagar, 2018. "Two Time-Scale Stochastic Approximation with Controlled Markov Noise and Off-Policy Temporal-Difference Learning," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 130-151, February.
    2. Yogesh Dahiya & Neeraja Sahasrabudhe, 2024. "Urns with Multiple Drawings and Graph-Based Interaction," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3283-3316, November.

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