Fully First-Order Methods for DecentralizedBilevel Optimization

Xiaoyu Wang

doi:10.1109/TSP.2025.3624427

Fully First-Order Methods for DecentralizedBilevel Optimization

2025-01-01

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DOI：10.1109/TSP.2025.3624427

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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.

Keywords:

Decentralized optimization

stochastic bilevel optimization

fully first-order method

gradient tracking

Fully First-Order Methods for DecentralizedBilevel Optimization

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