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Preprints, Working Papers, ... Year : 2023

A Kurdyka-Lojasiewicz property for stochastic optimization algorithms in a non-convex setting

Emilie Chouzenoux
Jean-Baptiste Fest
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  • PersonId : 1159534
Audrey Repetti
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  • PersonId : 1086960

Abstract

Stochastic differentiable approximation schemes are widely used for solving high dimensional problems. Most of existing methods satisfy some desirable properties, including conditional descent inequalities, and almost sure (a.s.) convergence guarantees on the objective function, or on the involved gradient. However, for non-convex objective functions, a.s. convergence of the iterates, i.e., the stochastic process, to a critical point is usually not guaranteed, and remains an important challenge. In this article, we develop a framework to bridge the gap between descent-type inequalities and a.s. convergence of the associated stochastic process. Leveraging a novel Kurdyka-Łojasiewicz property, we show convergence guarantees of stochastic processes under mild assumptions on the objective function. We also provide examples of stochastic algorithms benefiting from the proposed framework and derive a.s. convergence guarantees on the iterates.
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Dates and versions

hal-03992655 , version 1 (16-02-2023)

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Emilie Chouzenoux, Jean-Baptiste Fest, Audrey Repetti. A Kurdyka-Lojasiewicz property for stochastic optimization algorithms in a non-convex setting. 2023. ⟨hal-03992655⟩
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