# Communication-Efficient Federated Hypergradient Computation via Aggregated Iterative Differentiation

arXiv: https://arxiv.org/abs/2302.04969 · HTML: https://mlsanity.com/paper/2302.04969/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 66 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 30 of 44)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [Federated Optimization:Distributed Optimization Beyond the Datacenter](https://mlsanity.com/paper/1511.03575/) (2015)
- [Truncated Back-propagation for Bilevel Optimization](https://mlsanity.com/paper/1810.10667/) (2018)
- [Qsparse-local-SGD: Distributed SGD with Quantization, Sparsification, and Local Computations](https://mlsanity.com/paper/1906.02367/) (2019)
- [On the Iteration Complexity of Hypergradient Computation](https://mlsanity.com/paper/2006.16218/) (2020)
- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradients](https://mlsanity.com/paper/2102.07053/) (2021)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [FedSplit: An algorithmic framework for fast federated optimization](https://mlsanity.com/paper/2005.05238/) (2020)
- [Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithms](https://mlsanity.com/paper/1808.07576/) (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)

## Built on by (most cited first, 13 of 13)

- [Achieving Linear Speedup in Non-IID Federated Bilevel Learning](https://mlsanity.com/paper/2302.05412/) (2023)
- [Near-Optimal Nonconvex-Strongly-Convex Bilevel Optimization with Fully First-Order Oracles](https://mlsanity.com/paper/2306.14853/) (2023)
- [SimFBO: Towards Simple, Flexible and Communication-efficient Federated Bilevel Learning](https://mlsanity.com/paper/2305.19442/) (2023)
- [Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems](https://mlsanity.com/paper/2302.06701/) (2023)
- [LDC-MTL: Balancing Multi-Task Learning through Scalable Loss Discrepancy Control](https://mlsanity.com/paper/2502.08585/) (2025)
- [Efficient Federated Learning against Byzantine Attacks and Data Heterogeneity via Aggregating Normalized Gradients](https://mlsanity.com/paper/2408.09539/) (2024)
- [Multi-Objective Bilevel Learning](https://mlsanity.com/paper/2511.07824/) (2025)
- [Sequential Federated Learning in Hierarchical Architecture on Non-IID Datasets](https://mlsanity.com/paper/2408.09762/) (2024)
- [On the Fast Adaptation of Delayed Clients in Decentralized Federated Learning: A Centroid-Aligned Distillation Approach](https://mlsanity.com/paper/2508.02993/) (2025)
- [H+: An Efficient Similarity-Aware Aggregation for Byzantine Resilient Federated Learning](https://mlsanity.com/paper/2509.24330/) (2025)
- [Federated Multi-Sequence Stochastic Approximation with Local Hypergradient Estimation](https://mlsanity.com/paper/2306.01648/) (2023)
- [Dimensionality Reduction for Robust Federated Learning: A Theoretical Analysis and Convergence Guarantee](https://mlsanity.com/paper/2605.28335/) (2026)
- [From Data Heterogeneity to Convergence: A Data-Centric Review of Federated Learning](https://mlsanity.com/paper/2606.10595/) (2026)

## Abstract (arXiv)

Federated bilevel optimization has attracted increasing attention due to emerging machine learning and communication applications. The biggest challenge lies in computing the gradient of the upper-level objective function (i.e., hypergradient) in the federated setting due to the nonlinear and distributed construction of a series of global Hessian matrices. In this paper, we propose a novel communication-efficient federated hypergradient estimator via aggregated iterative differentiation (AggITD). AggITD is simple to implement and significantly reduces the communication cost by conducting the federated hypergradient estimation and the lower-level optimization simultaneously. We show that the proposed AggITD-based algorithm achieves the same sample complexity as existing approximate implicit differentiation (AID)-based approaches with much fewer communication rounds in the presence of data heterogeneity. Our results also shed light on the great advantage of ITD over AID in the federated/distributed hypergradient estimation. This differs from the comparison in the non-distributed bilevel optimization, where ITD is less efficient than AID. Our extensive experiments demonstrate the great effectiveness and communication efficiency of the proposed method.