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    This study introduces stable stochastic conjugate gradient (SCG) algorithms for machine learning. These methods improve convergence speed and stability in stochastic settings, outperforming existing optimization techniques.

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    Area of Science:

    • Optimization Algorithms
    • Machine Learning
    • Numerical Analysis

    Background:

    • Conjugate gradient (CG) is effective for large-scale machine learning but unstable in stochastic settings with noisy gradients.
    • Existing CG variants are not designed for stochastic optimization, leading to instability and divergence.

    Purpose of the Study:

    • To develop stable stochastic conjugate gradient (SCG) algorithms for mini-batch settings.
    • To enhance convergence rates and stability using variance reduction and adaptive step sizes.
    • To address limitations of line search in stochastic CG methods.

    Main Methods:

    • Introduced a novel class of stable stochastic CG (SCG) algorithms.
    • Employed variance-reduced techniques for improved stability.
    • Utilized the random stabilized Barzilai-Borwein (RSBB) method for online step size determination, replacing traditional line search.
    • Analyzed convergence properties rigorously.

    Main Results:

    • Proposed SCG algorithms achieve linear convergence rates in both strongly convex and nonconvex settings.
    • The algorithms exhibit computational complexity comparable to modern stochastic optimization methods.
    • Numerical experiments show superior performance against state-of-the-art stochastic optimization algorithms on machine learning tasks.

    Conclusions:

    • The developed SCG algorithms offer a stable and efficient approach for stochastic optimization in machine learning.
    • These algorithms provide a faster convergence rate and better stability compared to existing methods.
    • The RSBB method effectively replaces time-consuming line searches in stochastic settings.