Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems

Mohammad Partohaghighi, Roummel Marcia, YangQuan Chen

O‘zbekiston matematika jurnali · 2025-yil

Annotatsiya

Fractional-order stochastic gradient descent (FOSGD) leverages fractional exponents to capture long-memory effects in optimization. However, its utility is often limited by the difficulty of tuning and stabilizing these exponents. We propose 2SED Fractional-Order Stochastic Gradient Descent (2SEDFOSGD), which integrates the Two-Scale Effective Dimension (2SED) algorithm with FOSGD to adapt the fractional exponent in a data-driven manner. By tracking model sensitivity and effective dimensionality, 2SEDFOSGD dynamically modulates the exponent to mitigate oscillations and hasten convergence. Theoretically, this approach preserves the advantages of fractional memory without the sluggish or unstable behavior observed in na\"ive fractional SGD. Empirical evaluations in Gaussian and $\alpha$-stable noise scenarios using an autoregressive (AR) model,highlight faster convergence and more robust parameter estimates compared to baseline methods, underscoring the potential of dimension-aware fractional techniques for advanced modeling and estimation tasks.

Maqola ma’lumotlari
MualliflarMohammad Partohaghighi, Roummel Marcia, YangQuan Chen
JurnalO‘zbekiston matematika jurnali
NashriyotЎзбекистон Республикаси ФА Математика институти
ISSN2010-7269
Nashr sanasi2025-09-05
Jild69
Son3
Betlar142-152
TilIngliz
Ilmiy sohaFizika-matematika
DOI10.29229/uzmj.2025-3-15
Indeksga qo‘shilgan2026-08-26

DOI: 10.29229/uzmj.2025-3-15 · Maqolaning asl sahifasi

Kalit so‘zlar

Fractional Calculus, Stochastic Gradient Descent, Two Scale Effective Dimension, More Optimal Optimization

Ilmiy soha

Fizika-matematika

Iqtibos keltirish

APAMohammad Partohaghighi, Roummel Marcia, & YangQuan Chen (2025). Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems. O‘zbekiston matematika jurnali, 69(3), 142-152. https://doi.org/10.29229/uzmj.2025-3-15
GOST (OAK)Mohammad Partohaghighi, Roummel Marcia, YangQuan Chen Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 3. – P. 142-152. – DOI: 10.29229/uzmj.2025-3-15.
MLAMohammad Partohaghighi, Roummel Marcia, and YangQuan Chen. “Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems.” O‘zbekiston matematika jurnali, 69(3), 142-152, 2025. https://doi.org/10.29229/uzmj.2025-3-15
ChicagoMohammad Partohaghighi, Roummel Marcia, and YangQuan Chen. “Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems.” O‘zbekiston matematika jurnali, 69(3), 142-152 (2025). https://doi.org/10.29229/uzmj.2025-3-15
HarvardMohammad Partohaghighi, Roummel Marcia, and YangQuan Chen (2025) ‘Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems’, O‘zbekiston matematika jurnali, 69(3), 142-152. https://doi.org/10.29229/uzmj.2025-3-15
BibTeX
@article{mohammadpartohaghighi2025,
  title = {Effective Dimension Aware Fractional-Order Stochastic Gradient Descent for Convex Optimization Problems},
  author = {Mohammad Partohaghighi and Roummel Marcia and YangQuan Chen},
  journal = {O‘zbekiston matematika jurnali},
  year = {2025},
  volume = {69},
  number = {3},
  pages = {142-152},
  doi = {10.29229/uzmj.2025-3-15},
  url = {https://doi.org/10.29229/uzmj.2025-3-15}
}

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