Kalman Filter Enhanced GRPO for Reinforcement Learning-Based Language Model Reasoning

• URL: http://arxiv.org/abs/2505.07527v3
• Date: Wed, 24 Sep 2025 02:31:07 GMT
• Title: Kalman Filter Enhanced GRPO for Reinforcement Learning-Based Language Model Reasoning
• Authors: Hu Wang, Congbo Ma, Ian Reid, Mohammad Yaqub,
• Abstract summary: Group Relative Policy Optimization ( GRPO) was proposed to compute the advantage for each output by subtracting the mean reward, as the baseline, for all outputs in the group.<n>We show that using a more adaptive advantage estimation model, KRPO can improve the stability and performance of GRPO.
• Score: 11.157278744897427
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The advantage function is a central concept in RL that helps reduce variance in policy gradient estimates. Recently, for language modeling, Group Relative Policy Optimization (GRPO) was proposed to compute the advantage for each output by subtracting the mean reward, as the baseline, for all outputs in the group. However, it can lead to high variance when the reward advantage is inaccurately predicted. In this work, we propose Kalman Filter Enhanced Group Relative Policy Optimization (KRPO) model, by using lightweight Kalman filtering to dynamically estimate the latent reward baseline and uncertainty. This filtering technique replaces the naive group mean, enabling more adaptive advantage normalization. Our method does not require additional learned parameters over GRPO. This approach offers a simple yet effective way to incorporate multiple outputs of GRPO into advantage estimation, improving policy optimization in settings where highly dynamic reward signals are difficult to model for language models. Through the accuracies and rewards obtained from math question answering and reasoning, we show that using a more adaptive advantage estimation model, KRPO can improve the stability and performance of GRPO. The code is available at https://github.com/billhhh/KRPO_LLMs_RL.

Related papers

• Unbiased Dynamic Pruning for Efficient Group-Based Policy Optimization [60.87651283510059]
  Group Relative Policy Optimization (GRPO) effectively scales LLM reasoning but incurs prohibitive computational costs.<n>We propose Dynamic Pruning Policy Optimization (DPPO), a framework that enables dynamic pruning while preserving unbiased gradient estimation.<n>To mitigate the data sparsity induced by pruning, we introduce Dense Prompt Packing, a window-based greedy strategy.
  arXiv  Detail & Related papers  (2026-03-04T14:48:53Z)
• iGRPO: Self-Feedback-Driven LLM Reasoning [88.83313431248473]
  Large Language Models (LLMs) have shown promise in solving complex mathematical problems, yet they still fall short of producing accurate and consistent solutions.<n>We introduce Iterative Group Relative Policy Optimization (iGRPO), a two-stage extension of GRPO that adds dynamic self-conditioning through model-generated drafts.<n>Under matched rollout budgets, iGRPO consistently outperforms GRPO across base models.
  arXiv  Detail & Related papers  (2026-02-09T18:45:11Z)
• Rethinking the Trust Region in LLM Reinforcement Learning [72.25890308541334]
  Proximal Policy Optimization (PPO) serves as the de facto standard algorithm for Large Language Models (LLMs)<n>We propose Divergence Proximal Policy Optimization (DPPO), which substitutes clipping with a more principled constraint.<n>DPPO achieves superior training and efficiency compared to existing methods, offering a more robust foundation for RL-based fine-tuning.
  arXiv  Detail & Related papers  (2026-02-04T18:59:04Z)
• GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization [133.27496265096445]
  We show how to apply Group Relative Policy Optimization under multi-reward setting without examining its suitability.<n>We then introduce Group reward-Decoupled Normalization Policy Optimization (GDPO), a new policy optimization method to resolve these issues.<n>GDPO consistently outperforms GRPO, demonstrating its effectiveness and generalizability for multi-reward reinforcement learning optimization.
  arXiv  Detail & Related papers  (2026-01-08T18:59:24Z)
• $λ$-GRPO: Unifying the GRPO Frameworks with Learnable Token Preferences [22.199479724764725]
  We introduce a learnable parameter $lambda$ that adaptively controls token-level weighting.<n>We find that $lambda$-GRPO achieves consistent improvements over vanilla GRPO and DAPO.<n>These gains come without any modifications to the training data or additional computational cost.
  arXiv  Detail & Related papers  (2025-10-08T10:39:07Z)
• Geometric-Mean Policy Optimization [117.05113769757172]
  Group Relative Policy Optimization ( GRPO) has significantly enhanced the reasoning capability of large language models.<n> GRPO is observed to suffer from unstable policy updates when facing tokens with outlier importance-weighted rewards.<n>We propose Geometric-Mean Policy Optimization (GMPO) to improve the stability of GRPO through suppressing token reward outliers.
  arXiv  Detail & Related papers  (2025-07-28T09:54:05Z)
• On-Policy RL with Optimal Reward Baseline [109.47676554514193]
  On-Policy RL with Optimal reward baseline (OPO) is a novel and simplified reinforcement learning algorithm.<n>OPO emphasizes the importance of exact on-policy training, which empirically stabilizes the training process and enhances exploration.<n>Results demonstrate OPO's superior performance and training stability without additional models or regularization terms.
  arXiv  Detail & Related papers  (2025-05-29T15:58:04Z)
• Accelerating RL for LLM Reasoning with Optimal Advantage Regression [52.0792918455501]
  We propose a novel two-stage policy optimization framework that directly approximates the optimal advantage function.<n>$A$*-PO achieves competitive performance across a wide range of mathematical reasoning benchmarks.<n>It reduces training time by up to 2$times$ and peak memory usage by over 30% compared to PPO, GRPO, and REBEL.
  arXiv  Detail & Related papers  (2025-05-27T03:58:50Z)
• Not All Rollouts are Useful: Down-Sampling Rollouts in LLM Reinforcement Learning [55.15106182268834]
  Reinforcement learning with verifiable rewards (RLVR) has emerged as the leading approach for enhancing reasoning capabilities in large language models.<n>It faces a fundamental compute and memory asymmetry: rollout generation is embarrassingly parallel and memory-light, whereas policy updates are communication-heavy and memory-intensive.<n>We introduce PODS (Policy Optimization with Down-Sampling), which decouples rollout generation from policy updates by training only on a strategically selected subset of rollouts.
  arXiv  Detail & Related papers  (2025-04-18T17:49:55Z)
• A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce [68.99924691391048]
  We revisit GRPO from a reinforce-like algorithm perspective and analyze its core components.<n>We find that a simple rejection sampling baseline, RAFT, yields competitive performance than GRPO and PPO.<n>Motivated by this insight, we propose Reinforce-Rej, a minimal extension of policy gradient that filters both entirely incorrect and entirely correct samples.
  arXiv  Detail & Related papers  (2025-04-15T16:15:02Z)
• Optimizing Safe and Aligned Language Generation: A Multi-Objective GRPO Approach [2.8626097661711394]
  Reinforcement Learning from Human Feedback has achieved notable success in steering models, but is complex and can be unstable.<n>Recent approaches such as Direct Preference Optimization (DPO) simplify preference-based fine-tuning but may introduce bias or trade-off certain objectives.<n>We propose a Group Relative Policy Optimization framework with a multi-label reward regression model to achieve safe and aligned language generation.
  arXiv  Detail & Related papers  (2025-03-26T05:50:33Z)
• Lean and Mean: Decoupled Value Policy Optimization with Global Value Guidance [52.65461207786633]
  Policy-based Reinforcement Learning from Human Feedback is essential for aligning large language models with human preferences.<n>It requires joint training of an actor and critic with a pretrained, fixed reward model for guidance.<n>We propose textbfDecoupled Value Policy Optimization (DVPO), a lean framework that replaces traditional reward modeling with a pretrained emphglobal value model (GVM)
  arXiv  Detail & Related papers  (2025-02-24T08:11:33Z)
• $α$-DPO: Adaptive Reward Margin is What Direct Preference Optimization Needs [45.46582930202524]
  $alpha$-DPO is an adaptive preference optimization algorithm for large language models. It balances the policy model and the reference model to achieve personalized reward margins. It consistently outperforms DPO and SimPO across various model settings.
  arXiv  Detail & Related papers  (2024-10-14T04:29:57Z)
• Zeroth-Order Policy Gradient for Reinforcement Learning from Human Feedback without Reward Inference [15.038210624870656]
  Reward inference is a critical intermediate step in the Reinforcement Learning from Human Feedback pipeline.<n>This paper develops two RLHF algorithms without reward inference for general RL problems beyond bandits and deterministic MDP bandit, and general preference models beyond the Bradley-Terry model.
  arXiv  Detail & Related papers  (2024-09-25T22:20:11Z)
• Policy Filtration for RLHF to Mitigate Noise in Reward Models [27.278933096153974]
  Policy filtering for Proximal Policy Optimization (PF-PPO)<n>PF-PPO improves the signal-to-noise ratio during policy learning.<n>We provide experiments to validate the effectiveness of PF-PPO in code generation and math reasoning tasks.
  arXiv  Detail & Related papers  (2024-09-11T02:40:38Z)
• Provably Mitigating Overoptimization in RLHF: Your SFT Loss is Implicitly an Adversarial Regularizer [52.09480867526656]
  We identify the source of misalignment as a form of distributional shift and uncertainty in learning human preferences.<n>To mitigate overoptimization, we first propose a theoretical algorithm that chooses the best policy for an adversarially chosen reward model.<n>Using the equivalence between reward models and the corresponding optimal policy, the algorithm features a simple objective that combines a preference optimization loss and a supervised learning loss.
  arXiv  Detail & Related papers  (2024-05-26T05:38:50Z)
• Self-Play Preference Optimization for Language Model Alignment [75.83359213697854]
  Recent advancements suggest that directly working with preference probabilities can yield a more accurate reflection of human preferences. We propose a self-play-based method for language model alignment, which treats the problem as a constant-sum two-player game. Our approach, dubbed Self-Play Preference Optimization (SPPO), utilizes iterative policy updates to provably approximate the Nash equilibrium.
  arXiv  Detail & Related papers  (2024-05-01T17:59:20Z)
• REBEL: Reinforcement Learning via Regressing Relative Rewards [59.68420022466047]
  We propose REBEL, a minimalist RL algorithm for the era of generative models.<n>In theory, we prove that fundamental RL algorithms like Natural Policy Gradient can be seen as variants of REBEL.<n>We find that REBEL provides a unified approach to language modeling and image generation with stronger or similar performance as PPO and DPO.
  arXiv  Detail & Related papers  (2024-04-25T17:20:45Z)
• Preference as Reward, Maximum Preference Optimization with Importance Sampling [3.7040071165219595]
  We propose a simple and intuitive off-policy preference optimization algorithm from an importance sampling view, which we call Maximum Preference Optimization (MPO) MPO achieves the best of both worlds by combining the objectives of RLHF and IPO while being an off-policy algorithm.
  arXiv  Detail & Related papers  (2023-12-27T06:34:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.