Group Relative Policy Optimization (GRPO) has emerged as a powerful algorithm for improving the reasoning capabilities of language models, but often fails to improve small models due to sparse rewards on difficult tasks. Existing works mitigate this issue by leveraging a larger model, either to provide hints for rollouts or to provide dense reward signals through knowledge distillation (KD). However, this assumes the existence of such an oracle, and training one can significantly increase total training time. In this work, we propose CoDistill-GRPO, a co-distillation algorithm that simultaneously trains a large and a small model by maximizing carefully designed GRPO objectives. The two models learn from each other: the small model uses an on-policy KD reward to learn from the large model's distribution, while the large model is updated using rollouts generated by the small model with importance reweighting, reducing the computational overhead of rollout generation. We show that CoDistill-GRPO substantially improves small model performance over standard GRPO on mathematical benchmarks across both Qwen and Llama models. Specifically, with Qwen2.5-Math-1.5B, we observe an accuracy increase of over 11.6 percentage points over the base model and an additional 6.0 percentage points over GRPO on the Minerva dataset. Interestingly, the larger model (Qwen2.5-Math-7B) trained with CoDistill-GRPO nearly matches standard GRPO performance despite training on small-model rollouts. This highlights CoDistill-GRPO as a cost-effective alternative to GRPO for larger models, yielding an approximate 18% speedup, which may be of independent interest.

Group Relative Policy Optimization (GRPO) is a promising policy-based approach for Large Language Model alignment, yet its performance is often limited by training instability and suboptimal convergence. In this paper, we identify and analyze two main GRPO issues: (i) the token-level penalization, where valuable tokens shared across different responses receive contradictory feedback signals, leading to conflicting gradient updates that can reduce their likelihood; and (ii) the policy collapse, where negatively rewarded completions may penalize confident responses and shift model decisions toward unlikely tokens, destabilizing training process. To address these issues we introduce GTPO (Group-relative Trajectory-based Policy Optimization), which prevents conflicting gradients on valuable tokens by skipping negative updates while amplifying positive ones and filters out completions whose entropy exceeds a provable threshold, to prevent policy collapse. Unlike GRPO, GTPO does not rely on KL-divergence regularization, eliminating the need for a reference model during training, while still ensuring greater training stability and improved performance, as validated through multiple experiments on GSM8K, MA TH, AIME 2024, AIME 2025 and AMC 2023.

Post-training with reinforcement learning (RL) typically optimizes a single scalar objective and ignores structure in how solutions are produced. We ask whether a scalar hint toward a canonical solver ordering, used only during RL post-training, improves performance even when fine-tuned on randomized solution sequences. On Sudoku, we train a Transformer with standard fine-tuning on randomized solving orders, then post-train it with Group Relative Policy Optimization (GRPO) with two rewards: cell accuracy and an ordering reward that increases when the model's emission order aligns with the solver order. To compare signals cleanly, we combine them via fixed mixtures and use a simple bootstrapped scaling to equalize component magnitudes at initialization. Mixed rewards generally outperform cell-only optimization--the best mixture yields substantially higher test accuracy than the fine-tuned-only model trained on random-order and approaches the fine-tuned-only model trained on solver-order sequences in accuracy. These results suggest that coarse ordering signals can steer RL post-training toward solver-order trajectories without modifying supervised data or architecture.

Generating complex, logically-sound SPARQL queries for multi-hop questions remains a critical bottleneck for Knowledge Graph Question Answering, as the brittle nature of one-shot generation by Large Language Models (LLMs) hinders reliable interaction with structured data. Current methods lack the adaptive policies needed to dynamically debug queries based on real-time execution feedback. This paper introduces a novel agentic framework where an LLM learns a resilient policy for the sequential process of iterative SPARQL construction. We show that a compact 3B-parameter model, trained exclusively via outcome-driven Reinforcement Learning (GRPO) without supervised fine-tuning, can learn effective policies for this task, discovering how to systematically recover from execution errors and refine its queries toward a correct answer. On a curated, executable single-answer subset of LC-QuAD 2.0, our agent achieves 49.7\% accuracy post-entity-linking, a significant 17.5 percentage point improvement over the strongest iterative zero-shot baseline. Further analysis reveals that while the agent's capability is driven by RL, its performance is enhanced by an explicit deliberative reasoning step that acts as a cognitive scaffold to improve policy precision. This work presents a generalizable blueprint for teaching agents to master formal, symbolic tools through interaction, bridging the gap between probabilistic LLMs and the structured world of Knowledge Graphs.

Large Language Models (LLMs) often exhibit implicit biases and discriminatory tendencies that reflect underlying social stereotypes. While recent alignment techniques such as RLHF and DPO have mitigated some of these issues, they remain limited in addressing culturally specific and multi-dimensional forms of discrimination. This paper proposes a Multi-Reward Group Relative Policy Optimization (GRPO) framework to fine-tune LLMs toward ethical and bias-free behavior. Our approach constructs a synthetic English-language dataset derived from Chinese-context discrimination categories, including regional, ethnic, and occupational biases. Each instance is paired with both neutral and biased responses to train a reward model based on DeBERTa-v3, which provides multi-dimensional reward signals capturing fairness, neutrality, and linguistic quality. The trained reward model then guides GRPO fine-tuning to optimize model outputs along these ethical dimensions. Experimental results demonstrate significant reductions in bias intensity and improved alignment with non-discriminatory standards without compromising fluency or informativeness. This study highlights the effectiveness of GRPO-based multi-reward optimization for de-biasing LLMs and offers a replicable framework for cultural-contextual ethical alignment.

Reinforcement learning from verifiable rewards has emerged as a powerful technique for enhancing the complex reasoning abilities of Large Language Models (LLMs). However, these methods are fundamentally constrained by the ''learning cliff'' phenomenon: when faced with problems far beyond their current capabilities, models consistently fail, yielding a persistent zero-reward signal. In policy optimization algorithms like GRPO, this collapses the advantage calculation to zero, rendering these difficult problems invisible to the learning gradient and stalling progress. To overcome this, we introduce Scaf-GRPO (Scaffolded Group Relative Policy Optimization), a progressive training framework that strategically provides minimal guidance only when a model's independent learning has plateaued. The framework first diagnoses learning stagnation and then intervenes by injecting tiered in-prompt hints, ranging from abstract concepts to concrete steps, enabling the model to construct a valid solution by itself. Extensive experiments on challenging mathematics benchmarks demonstrate Scaf-GRPO's effectiveness, boosting the pass@1 score of the Qwen2.5-Math-7B model on the AIME24 benchmark by a relative 44.3% over a vanilla GRPO baseline. This result demonstrates our framework provides a robust and effective methodology for unlocking a model's ability to solve problems previously beyond its reach, a critical step towards extending the frontier of autonomous reasoning in LLM.

Traditional Chinese Medicine (TCM) presents a rich and structurally unique knowledge system that challenges conventional applications of large language models (LLMs). Although previous TCM - specific LLMs have shown progress through supervised fine - tuning, they often face limitations in alignment, data quality, and evaluation consistency. In this study, we introduce Ladder - base, the first TCM - focused LLM trained with Group Relative Policy Optimization (GRPO), a reinforcement learning method that improves reasoning and factual consistency by optimizing response selection based on intra - group comparisons. Ladder - base is built upon the Qwen2.5 - 7B - Instruct foundation model and trained exclusively on the textual subset of the TCM - Ladder benchmark, using 80 percent of the data for training and the remaining 20 percent split evenly between validation and test sets. Through standardized evaluation, Ladder - base demonstrates superior performance across multiple reasoning metrics when compared to both state - of - the - art general - purpose LLMs such as GPT - 4, Gemini 2.5, Claude 3, and Qwen3 and domain - specific TCM models including BenTsao, HuatuoGPT2, and Zhongjing. These findings suggest that GRPO provides an effective and efficient strategy for aligning LLMs with expert - level reasoning in traditional medical domains and supports the development of trustworthy and clinically grounded TCM artificial intelligence systems.

Inspired by the principle of self-regulating cooperation in collective institutions, we propose the Group Relative Policy Optimization with Global Cooperation Constraint (GRPO-GCC) framework. This work is the first to introduce GRPO into spatial public goods games, establishing a new deep reinforcement learning baseline for structured populations. GRPO-GCC integrates group relative policy optimization with a global cooperation constraint that strengthens incentives at intermediate cooperation levels while weakening them at extremes. This mechanism aligns local decision making with sustainable collective outcomes and prevents collapse into either universal defection or unconditional cooperation. The framework advances beyond existing approaches by combining group-normalized advantage estimation, a reference-anchored KL penalty, and a global incentive term that dynamically adjusts cooperative payoffs. As a result, it achieves accelerated cooperation onset, stabilized policy adaptation, and long-term sustainability. GRPO-GCC demonstrates how a simple yet global signal can reshape incentives toward resilient cooperation, and provides a new paradigm for multi-agent reinforcement learning in socio-technical systems.

The effective training of Large Language Models (LLMs) for function calling faces a critical challenge: balancing exploration of complex reasoning paths with stable policy optimization. Standard methods like Supervised Fine-Tuning (SFT) fail to instill robust reasoning, and traditional Reinforcement Learning (RL) struggles with inefficient exploration. We propose \textbf{EGPO}, a new RL framework built upon Group Relative Policy Optimization (GRPO), designed to address this challenge directly. The core of EGPO is an entropy-enhanced advantage function that integrates the entropy of the model's Chain-of-Thought (CoT) into the policy gradient computation. This encourages the generation of diverse reasoning strategies. To maintain optimization direction, the entropy bonus is carefully constrained by a clipping mechanism. Complemented by a strict, binary reward signal, EGPO effectively guides the model towards discovering structured and accurate tool invocation patterns. On the challenging Berkeley Function Calling Leaderboard (BFCL), a 4B-parameter model trained with EGPO sets a new state-of-the-art among models of comparable size, surpassing a range of strong competitors, including GPT-4o and Gemini-2.5.

Recent advances in Large Language Model (LLM) agents have demonstrated their promising general capabilities. However, their performance in specialized real-world domains often degrades due to challenges in effectively integrating external tools and specific prompting strategies. While methods like agentic reinforcement learning have been proposed to address this, they typically rely on costly parameter updates, for example, through a process that uses Supervised Fine-Tuning (SFT) followed by a Reinforcement Learning (RL) phase with Group Relative Policy Optimization (GRPO) to alter the output distribution. However, we argue that LLMs can achieve a similar effect on the output distribution by learning experiential knowledge as a token prior, which is a far more lightweight approach that not only addresses practical data scarcity but also avoids the common issue of overfitting. To this end, we propose Training-Free Group Relative Policy Optimization (Training-Free GRPO), a cost-effective solution that enhances LLM agent performance without any parameter updates. Our method leverages the group relative semantic advantage instead of numerical ones within each group of rollouts, iteratively distilling high-quality experiential knowledge during multi-epoch learning on a minimal ground-truth data. Such knowledge serves as the learned token prior, which is seamlessly integrated during LLM API calls to guide model behavior. Experiments on mathematical reasoning and web searching tasks demonstrate that Training-Free GRPO, when applied to DeepSeek-V3.1-Terminus, significantly improves out-of-domain performance. With just a few dozen training samples, Training-Free GRPO outperforms fine-tuned small LLMs with marginal training data and cost.