Fully First-Order Methods for DecentralizedBilevel Optimization

Xiaoyu Wang, Xuxing Chen, Shiqian Ma, Tong Zhang

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.

External IDs:dblp:journals/tsp/WangCMZ25