Fully First-Order Methods for Decentralized Bilevel Optimization
This addresses decentralized optimization for multi-agent systems, offering a more efficient alternative to second-order methods.
The paper tackles decentralized stochastic bilevel optimization by proposing DSGDA-GT, a first-order algorithm that achieves a sample complexity of O(n^{-1}ε^{-7}) for finding ε-stationary points, matching single-agent results with linear speedup.
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 $\mathcal{O}(n^{-1}ε^{-7})$, 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.