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    This study introduces a relaxed greedy algorithm for machine learning, offering faster learning rates than existing methods. The new algorithm also provides a clear stopping criterion, improving efficiency in handling noisy data.

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    Area of Science:

    • Machine Learning
    • Computational Learning Theory

    Background:

    • Traditional machine learning algorithms struggle with noisy data and imprecise targets, leading to high computational costs.
    • Greedy algorithms improve performance but have limitations in learning rate and stopping criteria.

    Purpose of the Study:

    • To introduce and analyze a novel relaxed greedy algorithm for machine learning.
    • To demonstrate improved learning rates and defined stopping criteria compared to existing greedy methods.

    Main Methods:

    • Development of a relaxed greedy algorithm.
    • Theoretical analysis of the algorithm's learning capability and convergence properties.

    Main Results:

    • The proposed relaxed greedy algorithm achieves a learning rate faster than the order m(-1/2).
    • The algorithm possesses a clearly defined stopping criterion, unlike many other greedy approaches.

    Conclusions:

    • The relaxed greedy algorithm offers a more efficient and decisive approach to machine learning with noisy data.
    • This advancement addresses computational burdens and sluggishness associated with traditional and existing greedy methods.