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    科学领域:

    • 优化理论 优化理论
    • 分布式系统 分布式系统
    • 机器学习 机器学习

    背景情况:

    • 现有的分布式优化算法通常需要全局的利普希茨连续性,这是不切实际的估计,可能不会持有.
    • 准确的利普希茨常数估计和全球假设的需要限制了当前方法的适用性和性能.

    研究的目的:

    • 为复合优化问题提出新的去中心化算法,即自适应式去中心化近似初级二元化 (ADPPD) 和自适应式去中心化初级二元化 (ADPD).
    • 通过消除对全球利普希茨连续性和过于保守的步骤大小的需求,克服现有方法的局限性.

    主要方法:

    • 开发了两种新的算法,ADPPD和ADPD,在改进的初级-双元框架内具有自适应式步骤大小.
    • 算法利用局部估计的协同强制性和利普希茨模块,避免全球假设.
    • 理论分析以确定凸和强烈凸场景的收率.

    主要成果:

    • 对于凸函数,ADPPD 实现了 $\mathcal {O}(1/k) $ 的 ergodic 收率.
    • 当光滑项强烈凸起时,ADPD显示了线性收率.
    • 在最小平方和逻辑回归上的数值实验证实了相对于现有方法的更快的趋同.

    结论:

    • 拟议的自适应式去中心化算法 (ADPPD和ADPD) 对于复合优化问题是有效的.
    • 这些算法通过利用本地Lipschitz连续性估计提供了更好的可扩展性和更快的融合.
    • 这些方法消除了对全球Lipschitz连续性的需求,提高了实际适用性.