# Decentralized Bilevel Optimization

arXiv: https://arxiv.org/abs/2206.05670 · HTML: https://mlsanity.com/paper/2206.05670/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2022.

## Built on by (most cited first, 23 of 23)

- [On Penalty-based Bilevel Gradient Descent Method](https://mlsanity.com/paper/2302.05185/) (2023)
- [Decentralized Stochastic Bilevel Optimization with Improved per-Iteration Complexity](https://mlsanity.com/paper/2210.12839/) (2022)
- [Achieving Linear Speedup in Non-IID Federated Bilevel Learning](https://mlsanity.com/paper/2302.05412/) (2023)
- [On the Convergence of Distributed Stochastic Bilevel Optimization Algorithms over a Network](https://mlsanity.com/paper/2206.15025/) (2022)
- [SimFBO: Towards Simple, Flexible and Communication-efficient Federated Bilevel Learning](https://mlsanity.com/paper/2305.19442/) (2023)
- [Asynchronous Distributed Bilevel Optimization](https://mlsanity.com/paper/2212.10048/) (2022)
- [Communication-Efficient Federated Hypergradient Computation via Aggregated Iterative Differentiation](https://mlsanity.com/paper/2302.04969/) (2023)
- [Alternating Implicit Projected SGD and Its Efficient Variants for Equality-constrained Bilevel Optimization](https://mlsanity.com/paper/2211.07096/) (2022)
- [Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems](https://mlsanity.com/paper/2302.06701/) (2023)
- [Fast Adaptive Federated Bilevel Optimization](https://mlsanity.com/paper/2211.01122/) (2022)
- [A Single-Loop Algorithm for Decentralized Bilevel Optimization](https://mlsanity.com/paper/2311.08945/) (2023)
- [Network Utility Maximization with Unknown Utility Functions: A Distributed, Data-Driven Bilevel Optimization Approach](https://mlsanity.com/paper/2301.01801/) (2023)
- [Efficient Curvature-Aware Hypergradient Approximation for Bilevel Optimization](https://mlsanity.com/paper/2505.02101/) (2025)
- [A Penalty-Based Method for Communication-Efficient Decentralized Bilevel Programming](https://mlsanity.com/paper/2211.04088/) (2022)
- [Argus: Federated Non-convex Bilevel Learning over 6G Space-Air-Ground Integrated Network](https://mlsanity.com/paper/2505.09106/) (2025)
- [Decentralized Hyper-Gradient Computation over Time-Varying Directed Networks](https://mlsanity.com/paper/2210.02129/) (2022)
- [Stochastic Nested Compositional Bi-level Optimization for Robust Feature Learning](https://mlsanity.com/paper/2307.05384/) (2023)
- [Fully First-Order Methods for Decentralized Bilevel Optimization](https://mlsanity.com/paper/2410.19319/) (2024)
- [Nonconvex Decentralized Stochastic Bilevel Optimization under Heavy-Tailed Noise](https://mlsanity.com/paper/2509.15543/) (2025)
- [DUET: Decentralized Bilevel Optimization without Lower-Level Strong Convexity](https://mlsanity.com/paper/2606.21153/) (2026)
- [Decentralized and Privacy-Preserving Learning of Approximate Stackelberg Solutions in Energy Trading Games with Demand Response Aggregators](https://mlsanity.com/paper/2304.02086/) (2023)
- [Federated Multi-Sequence Stochastic Approximation with Local Hypergradient Estimation](https://mlsanity.com/paper/2306.01648/) (2023)
- [S3LDBO: A Snapshot Single-Loop Algorithm for Decentralized Bilevel Optimization](https://mlsanity.com/paper/2605.31311/) (2026)

## Abstract (arXiv)

Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex bilevel optimization under a decentralized setting. We design decentralized algorithms for both deterministic and stochastic bilevel optimization problems. Moreover, we analyze the convergence rates of the proposed algorithms in difference scenarios including the case where data heterogeneity is observed across agents. Numerical experiments on both synthetic and real data demonstrate that the proposed methods are efficient.