Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex bilevel optimization under a decentralized setting. We design decentralized algorithms for both deterministic and stochastic bilevel optimization problems. Moreover, we analyze the convergence rates of the proposed algorithms in difference scenarios including the case where data heterogeneity is observed across agents. Numerical experiments on both synthetic and real data demonstrate that the proposed methods are efficient.

中文翻译：

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去中心化双层优化

双层优化已成功应用于许多重要的机器学习问题。已经在各种设置下研究了解决双层优化的算法。在本文中，我们研究了分散设置下的非凸强凸双层优化。我们为确定性和随机双层优化问题设计分散算法。此外，我们分析了所提出的算法在不同场景下的收敛速度，包括跨代理观察到数据异构性的情况。对合成数据和真实数据的数值实验表明所提出的方法是有效的。