Recent advances have demonstrated that integrating reinforcement learning with rule-based rewards can significantly enhance the reasoning capabilities of large language models, even without supervised fine-tuning. However, prevalent reinforcement learning algorithms such as GRPO and its variants like DAPO, suffer from a coarse granularity issue when computing the advantage. Specifically, they compute rollout-level advantages that assign identical values to every token within a sequence, failing to capture token-specific contributions and hindering effective learning. To address this limitation, we propose Key-token Advantage Estimation (KTAE) - a novel algorithm that estimates fine-grained, token-level advantages without introducing additional models. KTAE leverages the correctness of sampled rollouts and applies statistical analysis to quantify the importance of individual tokens within a sequence to the final outcome. This quantified token-level importance is then combined with the rollout-level advantage to obtain a more fine-grained token-level advantage estimation. Empirical results show that models trained with GRPO+KTAE and DAPO+KTAE outperform baseline methods across five mathematical reasoning benchmarks. Notably, they achieve higher accuracy with shorter responses and even surpass R1-Distill-Qwen-1.5B using the same base model.

Recent progress, such as DeepSeek-R1, has shown that the GRPO algorithm, a Reinforcement Learning (RL) approach, can effectively train Chain-of-Thought (CoT) reasoning in Large Language Models (LLMs) and Vision-Language Models (VLMs). In this paper, we analyze three challenges of GRPO: gradient coupling between thoughts and answers, sparse reward signals caused by limited parallel sampling, and unstable advantage estimation. To mitigate these challenges, we propose GRPO-MA, a simple yet theoretically grounded method that leverages multi-answer generation from each thought process, enabling more robust and efficient optimization. Theoretically, we show that the variance of thought advantage decreases as the number of answers per thought increases. Empirically, our gradient analysis confirms this effect, showing that GRPO-MA reduces gradient spikes compared to GRPO. Experiments on math, code, and diverse multimodal tasks demonstrate that GRPO-MA substantially improves performance and training efficiency. Our ablation studies further reveal that increasing the number of answers per thought consistently enhances model performance.

This paper investigates Reinforcement Learning (RL) approaches to enhance the reasoning capabilities of Large Language Model (LLM) agents in long-horizon, multi-turn scenarios. Although RL algorithms such as Group Relative Policy Optimization (GRPO) and Proximal Policy Optimization (PPO) have been widely applied to train multi-turn LLM agents, they typically rely only on sparse outcome rewards and lack dense intermediate signals across multiple decision steps, limiting their performance on complex reasoning tasks. To bridge this gap, we present the first systematic study of \textit{turn-level reward design} for multi-turn RL algorithms and agent applications. By integrating turn-level rewards, we extend GRPO and PPO to their respective multi-turn variants, enabling fine-grained credit assignment. We conduct case studies on multi-turn reasoning-augmented search agents, where we carefully design two types of turn-level rewards: verifiable and LLM-as-judge. Our experiments on multi-turn search tasks demonstrate that incorporating well-designed turn-level rewards enables RL algorithms to significantly outperform baseline methods with trajectory-level rewards. Both training and validation reward curves illustrate that our method achieves \textit{greater stability}, \textit{faster convergence}, and \textit{higher accuracy}. Numerical results across diverse question-answering datasets further show that our approach consistently delivers highest answer correctness and 100\% format correctness.

Enhancing the reasoning capabilities of large language models effectively using reinforcement learning (RL) remains a crucial challenge. Existing approaches primarily adopt two contrasting advantage estimation granularities: token-level methods (e.g., PPO) aim to provide fine-grained advantage signals but suffer from inaccurate estimation due to difficulties in training an accurate critic model. On the other extreme, trajectory-level methods (e.g., GRPO) solely rely on a coarse-grained advantage signal from the final reward, leading to imprecise credit assignment. To address these limitations, we propose Segment Policy Optimization (SPO), a novel RL framework that leverages segment-level advantage estimation at an intermediate granularity, achieving a better balance by offering more precise credit assignment than trajectory-level methods and requiring fewer estimation points than token-level methods, enabling accurate advantage estimation based on Monte Carlo (MC) without a critic model. SPO features three components with novel strategies: (1) flexible segment partition; (2) accurate segment advantage estimation; and (3) policy optimization using segment advantages, including a novel probability-mask strategy. We further instantiate SPO for two specific scenarios: (1) SPO-chain for short chain-of-thought (CoT), featuring novel cutpoint-based partition and chain-based advantage estimation, achieving $6$-$12$ percentage point improvements in accuracy over PPO and GRPO on GSM8K. (2) SPO-tree for long CoT, featuring novel tree-based advantage estimation, which significantly reduces the cost of MC estimation, achieving $7$-$11$ percentage point improvements over GRPO on MATH500 under 2K and 4K context evaluation. We make our code publicly available at https://github.com/AIFrameResearch/SPO.

Flow-based generative models have shown remarkable success in text-to-image generation, yet fine-tuning them with intermediate feedback remains challenging, especially for continuous-time flow matching models. Most existing approaches solely learn from outcome rewards, struggling with the credit assignment problem. Alternative methods that attempt to learn a critic via direct regression on cumulative rewards often face training instabilities and model collapse in online settings. We present AC-Flow, a robust actor-critic framework that addresses these challenges through three key innovations: (1) reward shaping that provides well-normalized learning signals to enable stable intermediate value learning and gradient control, (2) a novel dual-stability mechanism that combines advantage clipping to prevent destructive policy updates with a warm-up phase that allows the critic to mature before influencing the actor, and (3) a scalable generalized critic weighting scheme that extends traditional reward-weighted methods while preserving model diversity through Wasserstein regularization. Through extensive experiments on Stable Diffusion 3, we demonstrate that AC-Flow achieves state-of-the-art performance in text-to-image alignment tasks and generalization to unseen human preference models. Our results demonstrate that even with a computationally efficient critic model, we can robustly finetune flow models without compromising generative quality, diversity, or stability.

LLM-based multi-agent systems excel at planning, tool use, and role coordination, but their openness and interaction complexity also expose them to jailbreak, prompt-injection, and adversarial collaboration. Existing defenses fall into two lines: (i) self-verification that asks each agent to pre-filter unsafe instructions before execution, and (ii) external guard modules that police behaviors. The former often underperforms because a standalone agent lacks sufficient capacity to detect cross-agent unsafe chains and delegation-induced risks; the latter increases system overhead and creates a single-point-of-failure-once compromised, system-wide safety collapses, and adding more guards worsens cost and complexity. To solve these challenges, we propose AdvEvo-MARL, a co-evolutionary multi-agent reinforcement learning framework that internalizes safety into task agents. Rather than relying on external guards, AdvEvo-MARL jointly optimizes attackers (which synthesize evolving jailbreak prompts) and defenders (task agents trained to both accomplish their duties and resist attacks) in adversarial learning environments. To stabilize learning and foster cooperation, we introduce a public baseline for advantage estimation: agents within the same functional group share a group-level mean-return baseline, enabling lower-variance updates and stronger intra-group coordination. Across representative attack scenarios, AdvEvo-MARL consistently keeps attack-success rate (ASR) below 20%, whereas baselines reach up to 38.33%, while preserving-and sometimes improving-task accuracy (up to +3.67% on reasoning tasks). These results show that safety and utility can be jointly improved without relying on extra guard agents or added system overhead.

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.

Reinforcement Learning (RL) has achieved remarkable success across diverse domains, from game playing [1] to robotic control [2]. However, traditional policy optimization methods face significant challenges in continuous control settings, particularly in robotics where high-dimensional action spaces, sparse rewards, and sample inefficiency pose persistent obstacles [3]. Recent advances in policy optimization, such as Proximal Policy Optimization (PPO) [4] and Soft Actor-Critic (SAC) [5], have addressed key challenges through distinct techniques--PPO employs clipped surrogate objectives to ensure stable updates, while SAC leverages entropy regularization to encourage exploration and improve robustness. However, these methods rely heavily on value function approximation, which can introduce bias and instability, particularly in high-dimensional or sparse-reward environments common in robotics [6]. Group Relative Policy Optimization (GRPO) [7] presents an alternative approach by eliminating reliance on value function approximation through group-based advantage estimation. Initially developed for discrete action spaces, GRPO has demonstrated improved stability and sample efficiency in tasks such as language model alignment.