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 ϵ-stationary point in our algorithm is O(n−1ϵ−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.
@article{arxiv.2410.19319,
title = {Fully First-Order Methods for Decentralized Bilevel Optimization},
author = {Xiaoyu Wang and Xuxing Chen and Shiqian Ma and Tong Zhang},
journal= {arXiv preprint arXiv:2410.19319},
year = {2026}
}