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    This study provides theoretical learning rates for adaptive optimization algorithms like Adam, improving convergence for deep learning problems. Experiments show constant learning rates outperform diminishing ones in text and image tasks.

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    Area of Science:

    • Deep Learning
    • Stochastic Optimization

    Background:

    • Nonconvex stochastic optimization is crucial for deep learning.
    • Adaptive-learning-rate algorithms like Adam and AMSGrad are widely used but require appropriate learning rates.

    Purpose of the Study:

    • To derive theoretically grounded learning rates for adaptive optimization algorithms in nonconvex settings.
    • To demonstrate faster convergence compared to existing methods.
    • To evaluate the performance of constant versus diminishing learning rates.

    Main Methods:

    • Theoretical analysis of nonconvex stochastic optimization problems.
    • Development of adaptive learning rate strategies.
    • Numerical experiments on text and image classification tasks.

    Main Results:

    • New learning rates are proposed for algorithms like Adam and AMSGrad, enabling faster convergence.
    • Constant learning rates demonstrated superior performance over diminishing learning rates in practical deep learning applications.
    • Experimental validation on text and image classification confirmed theoretical findings.

    Conclusions:

    • The proposed learning rates offer theoretical and practical advantages for deep learning optimization.
    • Constant learning rates are recommended for adaptive optimization algorithms in deep learning tasks, challenging conventional approaches.