SPARKLE: A Unified Single-Loop Primal-Dual Framework for Decentralized Bilevel Optimization
This work addresses the problem of decentralized bilevel optimization for multiple agents collaborating on nested optimization tasks, offering incremental improvements over existing methods.
The paper tackles decentralized bilevel optimization by proposing SPARKLE, a unified single-loop primal-dual framework that allows flexible heterogeneity-correction strategies and mixed strategies for upper- and lower-level problems, achieving state-of-the-art convergence rates.
This paper studies decentralized bilevel optimization, in which multiple agents collaborate to solve problems involving nested optimization structures with neighborhood communications. Most existing literature primarily utilizes gradient tracking to mitigate the influence of data heterogeneity, without exploring other well-known heterogeneity-correction techniques such as EXTRA or Exact Diffusion. Additionally, these studies often employ identical decentralized strategies for both upper- and lower-level problems, neglecting to leverage distinct mechanisms across different levels. To address these limitations, this paper proposes SPARKLE, a unified Single-loop Primal-dual AlgoRithm frameworK for decentraLized bilEvel optimization. SPARKLE offers the flexibility to incorporate various heterogeneitycorrection strategies into the algorithm. Moreover, SPARKLE allows for different strategies to solve upper- and lower-level problems. We present a unified convergence analysis for SPARKLE, applicable to all its variants, with state-of-the-art convergence rates compared to existing decentralized bilevel algorithms. Our results further reveal that EXTRA and Exact Diffusion are more suitable for decentralized bilevel optimization, and using mixed strategies in bilevel algorithms brings more benefits than relying solely on gradient tracking.