# FedGRPO: Privately Optimizing Foundation Models with Group-Relative Rewards from Domain Client

arXiv: https://arxiv.org/abs/2602.12014 · HTML: https://mlsanity.com/paper/2602.12014/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [Multimodal Federated Learning via Contrastive Representation Ensemble](https://mlsanity.com/paper/2302.08888/) (2023)
- [pFedLoRA: Model-Heterogeneous Personalized Federated Learning with LoRA Tuning](https://mlsanity.com/paper/2310.13283/) (2023)
- [Advances and Open Challenges in Federated Foundation Models](https://mlsanity.com/paper/2404.15381/) (2024)
- [Grounding Foundation Models through Federated Transfer Learning: A General Framework](https://mlsanity.com/paper/2311.17431/) (2023)
- [Ten Challenging Problems in Federated Foundation Models](https://mlsanity.com/paper/2502.12176/) (2025)
- [Unveiling the Vulnerability of Private Fine-Tuning in Split-Based Frameworks for Large Language Models: A Bidirectionally Enhanced Attack](https://mlsanity.com/paper/2409.00960/) (2024)

## Abstract (arXiv)

One important direction of Federated Foundation Models (FedFMs) is leveraging data from small client models to enhance the performance of a large server-side foundation model. Existing methods based on model level or representation level knowledge transfer either require expensive local training or incur high communication costs and introduce unavoidable privacy risks. We reformulate this problem as a reinforcement learning style evaluation process and propose FedGRPO, a privacy preserving framework comprising two modules. The first module performs competence-based expert selection by building a lightweight confidence graph from auxiliary data to identify the most suitable clients for each question. The second module leverages the "Group Relative" concept from the Group Relative Policy Optimization (GRPO) framework by packaging each question together with its solution rationale into candidate policies, dispatching these policies to a selected subset of expert clients, and aggregating solely the resulting scalar reward signals via a federated group-relative loss function. By exchanging reward values instead of data or model updates, FedGRPO reduces privacy risk and communication overhead while enabling parallel evaluation across heterogeneous devices. Empirical results on diverse domain tasks demonstrate that FedGRPO achieves superior downstream accuracy and communication efficiency compared to conventional FedFMs baselines.