FGRPO: Federated GRPO with Adaptive Aggregation on Non-IID Data

Reinforcement learning methods such as GRPO have seen great popularity in LLM post-training. In GRPO, models produce completions to a set of prompts, which are rewarded, and the policy is updated towards the relatively high reward completions. Due to the auto-regressive nature of models, the generation phase of such style of training can be extremely time consuming. As a solution, prior work has sought to distribute the inference step across many nodes, working parallel. These works assume primarily homogeneous models in the training in order to keep samples as close to on-policy as possible. This assumption may be impractical in decentralized systems, where parties with various computes and preferences may wish to collaborate on the same task. Thus, decentralized training requires an approach that can handle heterogeneous models - different models collaborating on the same tasks. However, this leads to highly off-policy samples presented during training, which prior work has identified that off-policy samples can hurt GRPO convergence. To enable heterogeneity, we propose Filtered Truncated Importance Sampling (F-TIS) - a GRPO-style training paradigm that can use off-policy samples to improve local model's learning. Our framework allows various models to collaborate in the same RL training run while being communication efficient. We extensively evaluate F-TIS in various heterogeneous setups and we show that it exhibits identical final model convergence to purely on-sample training. Furthermore, we observe in some setups better generalization on out-of-distribution tasks than on-policy training, increasing model's performance by up to 12%.

Group Relative Policy Optimization (GRPO) has emerged as a promising approach for improving the reasoning capabilities of large language models. However, it struggles to effectively balance the tradeoff between exploration and exploitation during training, often resulting in suboptimal performance. Motivated by the theoretical insight that changes in entropy are governed by the covariance between token probabilities and their corresponding advantages, we propose a hyperparameter-free, covariance-weighted optimization method that dynamically down-weights extreme token-level updates via a Gaussian kernel. This approach automatically reduces the instability caused by exploration-exploitation trade-off while preserving informative learning signals. Extensive empirical evaluations show that our approach improves downstream performance across reasoning benchmarks compared with GRPO, and effectively stablizes entropy as training progresses.

Large language models (LLMs) exhibit strong reasoning capabilities when guided by high-quality demonstrations, yet such data is often distributed across organizations that cannot centralize it due to regulatory, proprietary, or institutional constraints. We study federated reasoning, where a server improves multi-step reasoning by coordinating with heterogeneous clients holding private demonstrations, without centralized training or raw data sharing. The key challenge is that client reliability is query-dependent, while the server cannot inspect client data to determine which contributions are trustworthy. To address this, we propose Uncertainty-Aware Federated Reasoning (FERA), a training-free framework based on iterative server-client co-refinement. Across communication rounds, clients generate reasoning traces with lightweight uncertainty estimates, and the server synthesizes them into improved reasoning that is redistributed as context for the next round, progressively improving both server outputs and client-side reasoning. Within each round, Uncertainty-Aware Self-Critique Aggregation (UA-SCA) resolves conflicts among heterogeneous client traces through query-dependent trust weighting and structured cross-client verification. Rather than simply discarding low-quality traces, UA-SCA revises flawed reasoning steps to recover useful information. We provide theoretical guarantees showing that the proposed iterative protocol converges and that uncertainty-aware weighting accelerates convergence. Experiments on multiple reasoning benchmarks show that FERA consistently outperforms both federated training and training-free baselines, achieving progressively higher accuracy across rounds while maintaining communication and computational efficiency.