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Almost sure convergence of stochastic gradient processes with matrix step sizes

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  • Monnez, Jean-Marie

Abstract

We consider a stochastic gradient process, which is a special case of stochastic approximation process, where the positive real step size an is replaced by a random matrix An: Xn+1=Xn-An[backward difference]g(Xn)-AnVn. We give two theorems of almost sure convergence in the case where the equation [backward difference]g=0 has a set of solutions.

Suggested Citation

  • Monnez, Jean-Marie, 2006. "Almost sure convergence of stochastic gradient processes with matrix step sizes," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 531-536, March.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:5:p:531-536
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    Cited by:

    1. Lorenzo Rosasco & Silvia Villa & Bang Công Vũ, 2016. "Stochastic Forward–Backward Splitting for Monotone Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 388-406, May.
    2. Cardot, Hervé & Cénac, Peggy & Monnez, Jean-Marie, 2012. "A fast and recursive algorithm for clustering large datasets with k-medians," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1434-1449.

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