# Provably Convergent Federated Trilevel Learning

arXiv: https://arxiv.org/abs/2312.11835 · HTML: https://mlsanity.com/paper/2312.11835/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 19 Dec 2023.

## Builds on (most cited first, 25 of 25)

- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Asynchronous Federated Optimization](https://mlsanity.com/paper/1903.03934/) (2019)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [When NAS Meets Robustness: In Search of Robust Architectures against Adversarial Attacks](https://mlsanity.com/paper/1911.10695/) (2019)
- [Adaptive Gradient Sparsification for Efficient Federated Learning: An Online Learning Approach](https://mlsanity.com/paper/2001.04756/) (2020)
- [Revisiting and Advancing Fast Adversarial Training Through The Lens of Bi-Level Optimization](https://mlsanity.com/paper/2112.12376/) (2021)
- [A Single-Timescale Method for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2102.04671/) (2021)
- [Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond](https://mlsanity.com/paper/2110.00455/) (2021)
- [FedNest: Federated Bilevel, Minimax, and Compositional Optimization](https://mlsanity.com/paper/2205.02215/) (2022)
- [A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems](https://mlsanity.com/paper/2006.02032/) (2020)
- [Hybrid Block Successive Approximation for One-Sided Non-Convex Min-Max Problems: Algorithms and Applications](https://mlsanity.com/paper/1902.08294/) (2019)
- [Advances in Asynchronous Parallel and Distributed Optimization](https://mlsanity.com/paper/2006.13838/) (2020)
- [Robust Optimization over Multiple Domains](https://mlsanity.com/paper/1805.07588/) (2018)
- [Meta-Learning to Improve Pre-Training](https://mlsanity.com/paper/2111.01754/) (2021)
- [Betty: An Automatic Differentiation Library for Multilevel Optimization](https://mlsanity.com/paper/2207.02849/) (2022)
- [Discriminative Feature Alignment: Improving Transferability of Unsupervised Domain Adaptation by Gaussian-guided Latent Alignment](https://mlsanity.com/paper/2006.12770/) (2020)
- [Distributed Distributionally Robust Optimization with Non-Convex Objectives](https://mlsanity.com/paper/2210.07588/) (2022)
- [A Gradient Method for Multilevel Optimization](https://mlsanity.com/paper/2105.13954/) (2021)
- [Learning from Mistakes -- A Framework for Neural Architecture Search](https://mlsanity.com/paper/2111.06353/) (2021)
- [FedAL: Black-Box Federated Knowledge Distillation Enabled by Adversarial Learning](https://mlsanity.com/paper/2311.16584/) (2023)
- [A Polyhedral Approximation Framework for Convex and Robust Distributed Optimization](https://mlsanity.com/paper/1303.6092/) (2013)

## Built on by (most cited first, 6 of 6)

- [PR-Attack: Coordinated Prompt-RAG Attacks on Retrieval-Augmented Generation in Large Language Models via Bilevel Optimization](https://mlsanity.com/paper/2504.07717/) (2025)
- [Tri-Level Navigator: LLM-Empowered Tri-Level Learning for Time Series OOD Generalization](https://mlsanity.com/paper/2410.07018/) (2024)
- [A stochastic gradient method for trilevel optimization](https://mlsanity.com/paper/2505.06805/) (2025)
- [Argus: Federated Non-convex Bilevel Learning over 6G Space-Air-Ground Integrated Network](https://mlsanity.com/paper/2505.09106/) (2025)
- [CHAL: Council of Hierarchical Agentic Language](https://mlsanity.com/paper/2605.12718/) (2026)
- [First-order Constrained Trilevel Optimization Over Distributed Networks for Robust Coreset Selection](https://mlsanity.com/paper/2607.27632/) (2026)

## Abstract (arXiv)

Trilevel learning, also called trilevel optimization (TLO), has been recognized as a powerful modelling tool for hierarchical decision process and widely applied in many machine learning applications, such as robust neural architecture search, hyperparameter optimization, and domain adaptation. Tackling TLO problems has presented a great challenge due to their nested decision-making structure. In addition, existing works on TLO face the following key challenges: 1) they all focus on the non-distributed setting, which may lead to privacy breach; 2) they do not offer any non-asymptotic convergence analysis which characterizes how fast an algorithm converges. To address the aforementioned challenges, this paper proposes an asynchronous federated trilevel optimization method to solve TLO problems. The proposed method utilizes μ-cuts to construct a hyper-polyhedral approximation for the TLO problem and solve it in an asynchronous manner. We demonstrate that the proposed μ-cuts are applicable to not only convex functions but also a wide range of non-convex functions that meet the μ-weakly convex assumption. Furthermore, we theoretically analyze the non-asymptotic convergence rate for the proposed method by showing its iteration complexity to obtain ε-stationary point is upper bounded by O(frac1ε2). Extensive experiments on real-world datasets have been conducted to elucidate the superiority of the proposed method, e.g., it has a faster convergence rate with a maximum acceleration of approximately 80%.