Fully First-Order Methods for Decentralized Bilevel Optimization

• URL: http://arxiv.org/abs/2410.19319v1
• Date: Fri, 25 Oct 2024 06:11:43 GMT
• Title: Fully First-Order Methods for Decentralized Bilevel Optimization
• Authors: Xiaoyu Wang, Xuxing Chen, Shiqian Ma, Tong Zhang,
• Abstract summary: This paper focuses on decentralized bilevel optimization (DSBO) where agents only communicate with their neighbors. We propose Decentralized Gradient Descent and Ascent with Gradient Tracking (DSGDA-GT), a novel algorithm that only requires first-order oracles that are much cheaper than second-order oracles widely adopted in existing works.
• Score: 17.20330936572045
• License:
• Abstract: This paper focuses on decentralized stochastic bilevel optimization (DSBO) where agents only communicate with their neighbors. We propose Decentralized Stochastic Gradient Descent and Ascent with Gradient Tracking (DSGDA-GT), a novel algorithm that only requires first-order oracles that are much cheaper than second-order oracles widely adopted in existing works. We further provide a finite-time convergence analysis showing that for $n$ agents collaboratively solving the DSBO problem, the sample complexity of finding an $\epsilon$-stationary point in our algorithm is $\mathcal{O}(n^{-1}\epsilon^{-7})$, which matches the currently best-known results of the single-agent counterpart with linear speedup. The numerical experiments demonstrate both the communication and training efficiency of our algorithm.

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