# Federated Multi-Level Optimization over Decentralized Networks

arXiv: https://arxiv.org/abs/2310.06217 · HTML: https://mlsanity.com/paper/2310.06217/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 29 of 29)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [Asynchronous Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06952/) (2017)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [Decentralized Deep Learning with Arbitrary Communication Compression](https://mlsanity.com/paper/1907.09356/) (2019)
- [Distributed Stochastic Gradient Tracking Methods](https://mlsanity.com/paper/1805.11454/) (2018)
- [A Near-Optimal Algorithm for Stochastic Bilevel Optimization via Double-Momentum](https://mlsanity.com/paper/2102.07367/) (2021)
- [Provably Faster Algorithms for Bilevel Optimization](https://mlsanity.com/paper/2106.04692/) (2021)
- [Accelerated Gradient Methods for Nonconvex Nonlinear and Stochastic Programming](https://mlsanity.com/paper/1310.3787/) (2013)
- [FedNest: Federated Bilevel, Minimax, and Compositional Optimization](https://mlsanity.com/paper/2205.02215/) (2022)
- [An improved convergence analysis for decentralized online stochastic non-convex optimization](https://mlsanity.com/paper/2008.04195/) (2020)
- [Accelerating Stochastic Composition Optimization](https://mlsanity.com/paper/1607.07329/) (2016)
- [Communication-Efficient Algorithms for Decentralized and Stochastic Optimization](https://mlsanity.com/paper/1701.03961/) (2017)
- [Provable Representation Learning for Imitation Learning via Bi-level Optimization](https://mlsanity.com/paper/2002.10544/) (2020)
- [An Asynchronous Mini-Batch Algorithm for Regularized Stochastic Optimization](https://mlsanity.com/paper/1505.04824/) (2015)
- [Variance-Reduced Decentralized Stochastic Optimization with Accelerated Convergence](https://mlsanity.com/paper/1912.04230/) (2019)
- [Randomized Stochastic Variance-Reduced Methods for Multi-Task Stochastic Bilevel Optimization](https://mlsanity.com/paper/2105.02266/) (2021)
- [Multi-Level Stochastic Gradient Methods for Nested Composition Optimization](https://mlsanity.com/paper/1801.03600/) (2018)
- [Finite-sum Composition Optimization via Variance Reduced Gradient Descent](https://mlsanity.com/paper/1610.04674/) (2016)
- [Random gradient extrapolation for distributed and stochastic optimization](https://mlsanity.com/paper/1711.05762/) (2017)
- [Periodic Stochastic Gradient Descent with Momentum for Decentralized Training](https://mlsanity.com/paper/2008.10435/) (2020)
- [On ℓp-hyperparameter Learning via Bilevel Nonsmooth Optimization](https://mlsanity.com/paper/1806.01520/) (2018)
- [Voting-Based Multi-Agent Reinforcement Learning for Intelligent IoT](https://mlsanity.com/paper/1907.01385/) (2019)
- [A Two-Stage Decomposition Approach for AC Optimal Power Flow](https://mlsanity.com/paper/2002.08003/) (2020)

## Abstract (arXiv)

Multi-level optimization has gained increasing attention in recent years, as it provides a powerful framework for solving complex optimization problems that arise in many fields, such as meta-learning, multi-player games, reinforcement learning, and nested composition optimization. In this paper, we study the problem of distributed multi-level optimization over a network, where agents can only communicate with their immediate neighbors. This setting is motivated by the need for distributed optimization in large-scale systems, where centralized optimization may not be practical or feasible. To address this problem, we propose a novel gossip-based distributed multi-level optimization algorithm that enables networked agents to solve optimization problems at different levels in a single timescale and share information through network propagation. Our algorithm achieves optimal sample complexity, scaling linearly with the network size, and demonstrates state-of-the-art performance on various applications, including hyper-parameter tuning, decentralized reinforcement learning, and risk-averse optimization.