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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Descenso de Gradiente Fraccional con Tamaños de Paso de Matriz para Optimización No Convexa

Alokendu Mazumder, Keshav Vyas, Punit Rathore

    IEEE transactions on neural networks and learning systems
    |December 12, 2025
    PubMed
    Resumen

    Este estudio presenta el descenso de gradiente fraccional (FGD) para funciones no convexas suaves de matriz, ofreciendo garantías de convergencia. Los algoritmos novedosos con tamaños de paso de matriz aceleran la convergencia en entornos distribuidos.

    Palabras clave:
    descenso de gradiente fraccionaloptimización no convexatamaños de paso de matrizaprendizaje automático distribuidoteoría de la optimización

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    Área de la Ciencia:

    • Teoría de la Optimización
    • Aprendizaje Automático
    • Optimización No Convexa

    Sus antecedentes:

    • Las derivadas fraccionales generalizan las derivadas de orden entero, relevantes para los algoritmos de optimización.
    • El análisis de convergencia existente para el descenso de gradiente fraccional (FGD) es limitado en alcance y entornos aplicables.
    • Los problemas de optimización no convexa son prevalentes en el aprendizaje automático y requieren algoritmos robustos.

    Objetivo del estudio:

    • Establecer garantías de convergencia para FGD en una clase más amplia de funciones no convexas (funciones suaves de matriz).
    • Proponer nuevos algoritmos estocásticos de descenso fraccional (CFGD) con tamaños de paso de valor de matriz.
    • Analizar la convergencia en entornos de un solo nodo y distribuidos para objetivos suaves de matriz.

    Principales métodos:

    • Aprovechamiento de las propiedades de suavidad de la matriz para probar la convergencia y acelerar las iteraciones de FGD.
    • Desarrollo de dos nuevos algoritmos estocásticos de descenso fraccional (CFGD).
    • Incorporación de tamaños de paso de valor de matriz para minimizar objetivos no convexos suaves de matriz.

    Principales resultados:

    • Se establecieron garantías de convergencia para FGD en funciones no convexas suaves de matriz.
    • Se demostró que los tamaños de paso de matriz conducen a una convergencia más rápida que los tamaños de paso escalares al capturar mejor la estructura del objetivo.
    • Se mostró la efectividad de los tamaños de paso de matriz para aprovechar la estructura del modelo.

    Conclusiones:

    • Este trabajo proporciona el primer análisis de convergencia de FGD para funciones no convexas suaves de matriz.
    • Se introdujeron nuevos algoritmos CFGD que superan a los métodos tradicionales en entornos distribuidos.
    • Se destacó la importancia de los tamaños de paso de matriz para una optimización eficiente en el aprendizaje federado/distribuido.