# Decentralized Hyper-Gradient Computation over Time-Varying Directed Networks

arXiv: https://arxiv.org/abs/2210.02129 · HTML: https://mlsanity.com/paper/2210.02129/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 33 references that are in the map.
- First posted on arXiv 5 Oct 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Stochastic Gradient Push for Distributed Deep Learning](https://mlsanity.com/paper/1811.10792/) (2018)
- [Distributed optimization over time-varying directed graphs](https://mlsanity.com/paper/1303.2289/) (2013)
- [FedNest: Federated Bilevel, Minimax, and Compositional Optimization](https://mlsanity.com/paper/2205.02215/) (2022)
- [Throughput-Optimal Topology Design for Cross-Silo Federated Learning](https://mlsanity.com/paper/2010.12229/) (2020)
- [Stochastic Gradient-Push for Strongly Convex Functions on Time-Varying Directed Graphs](https://mlsanity.com/paper/1406.2075/) (2014)
- [Decentralized Gossip-Based Stochastic Bilevel Optimization over Communication Networks](https://mlsanity.com/paper/2206.10870/) (2022)
- [Privacy Amplification by Decentralization](https://mlsanity.com/paper/2012.05326/) (2020)
- [Decentralized Bilevel Optimization](https://mlsanity.com/paper/2206.05670/) (2022)
- [Local Stochastic Bilevel Optimization with Momentum-Based Variance Reduction](https://mlsanity.com/paper/2205.01608/) (2022)
- [Toward Understanding the Influence of Individual Clients in Federated Learning](https://mlsanity.com/paper/2012.10936/) (2020)

## Built on by (most cited first, 1 of 1)

- [DICE: Data Influence Cascade in Decentralized Learning](https://mlsanity.com/paper/2507.06931/) (2025)

## Abstract (arXiv)

This paper addresses the communication issues when estimating hyper-gradients in decentralized federated learning (FL). Hyper-gradients in decentralized FL quantifies how the performance of globally shared optimal model is influenced by the perturbations in clients' hyper-parameters. In prior work, clients trace this influence through the communication of Hessian matrices over a static undirected network, resulting in (i) excessive communication costs and (ii) inability to make use of more efficient and robust networks, namely, time-varying directed networks. To solve these issues, we introduce an alternative optimality condition for FL using an averaging operation on model parameters and gradients. We then employ Push-Sum as the averaging operation, which is a consensus optimization technique for time-varying directed networks. As a result, the hyper-gradient estimator derived from our optimality condition enjoys two desirable properties; (i) it only requires Push-Sum communication of vectors and (ii) it can operate over time-varying directed networks. We confirm the convergence of our estimator to the true hyper-gradient both theoretically and empirically, and we further demonstrate that it enables two novel applications: decentralized influence estimation and personalization over time-varying networks.