Decentralized Bilevel Optimization over Graphs: Loopless Algorithmic Update and Transient Iteration Complexity

• URL: http://arxiv.org/abs/2402.03167v2
• Date: Mon, 26 Feb 2024 11:30:42 GMT
• Title: Decentralized Bilevel Optimization over Graphs: Loopless Algorithmic Update and Transient Iteration Complexity
• Authors: Boao Kong, Shuchen Zhu, Songtao Lu, Xinmeng Huang, Kun Yuan
• Abstract summary: We introduce a single-loop decentralized SBO (D-SOBA) algorithm and establish its transient complexity. D-SOBA achieves the state-of-the-art rate, gradient/Hessian complexity, and transient iteration complexity under more relaxed assumptions.
• Score: 38.54552875789929
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Stochastic bilevel optimization (SBO) is becoming increasingly essential in machine learning due to its versatility in handling nested structures. To address large-scale SBO, decentralized approaches have emerged as effective paradigms in which nodes communicate with immediate neighbors without a central server, thereby improving communication efficiency and enhancing algorithmic robustness. However, current decentralized SBO algorithms face challenges, including expensive inner-loop updates and unclear understanding of the influence of network topology, data heterogeneity, and the nested bilevel algorithmic structures. In this paper, we introduce a single-loop decentralized SBO (D-SOBA) algorithm and establish its transient iteration complexity, which, for the first time, clarifies the joint influence of network topology and data heterogeneity on decentralized bilevel algorithms. D-SOBA achieves the state-of-the-art asymptotic rate, asymptotic gradient/Hessian complexity, and transient iteration complexity under more relaxed assumptions compared to existing methods. Numerical experiments validate our theoretical findings.

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