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Incremental Without Replacement Sampling in Nonconvex Optimization

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  • Edouard Pauwels

    (Université de Toulouse)

Abstract

Minibatch decomposition methods for empirical risk minimization are commonly analyzed in a stochastic approximation setting, also known as sampling with replacement. On the other hand, modern implementations of such techniques are incremental: they rely on sampling without replacement, for which available analysis is much scarcer. We provide convergence guaranties for the latter variant by analyzing a versatile incremental gradient scheme. For this scheme, we consider constant, decreasing or adaptive step sizes. In the smooth setting, we obtain explicit complexity estimates in terms of epoch counter. In the nonsmooth setting, we prove that the sequence is attracted by solutions of optimality conditions of the problem.

Suggested Citation

  • Edouard Pauwels, 2021. "Incremental Without Replacement Sampling in Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 274-299, July.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:1:d:10.1007_s10957-021-01883-2
    DOI: 10.1007/s10957-021-01883-2
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    References listed on IDEAS

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    1. Bolte, Jérôme & Pauwels, Edouard, 2021. "A mathematical model for automatic differentiation in machine learning," TSE Working Papers 21-1184, Toulouse School of Economics (TSE).
    2. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
    3. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
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