Fed-GRPO: Reward-Signal-Driven Federated Group Relative Policy Optimization

Large Language Models (LLMs) have shown strong reasoning capabilities when fine-tuned with reinforcement learning (RL), particularly through Group Relative Policy Optimization (GRPO). However, existing GRPO methods assume centralized access to training data, which may not hold in practice due to privacy or regulatory constraints. To this end, we propose Fed-GRPO, a federated GRPO training framework that addresses these privacy constraints by enabling collaborative reasoning training without sharing raw data, which leverages the reward statistics naturally produced during GRPO training as zero-cost signals to guide aggregation, local training, and communication. Fed-GRPO contains three reward-signal-driven mechanisms: (i) signal-weighted aggregation that weights clients by their reward standard deviation, prioritizing clients with stronger learning signals; (ii) global reward calibration that re-weights per-prompt objectives based on the local-global reward gap, steering each client toward its relative weaknesses; and (iii) adaptive sparse communication that allocates bandwidth based on the informativeness of each client's update. Extensive experiments on mathematical reasoning tasks demonstrate that Fed-GRPO achieves the best performance among all federated methods, clearly outperforms FedAvg and approaches centralized training performance, while losslessly reducing communication by $32\times$ and supporting up to $621\times$ compression under tight bandwidth budgets with only graceful accuracy degradation.