Xiaodong Lu

Li Wang, Xiaodong Lu, Xiaohan Wang et al.

Large Language Models (LLMs) have achieved remarkable advancements in reasoning capabilities empowered by Reinforcement Learning with Verifiable Rewards (RLVR). Nonetheless, RLVR intrinsically relies on ground-truth labels for reward computation, the acquisition of which is often prohibitively expensive in real-world scenarios. While unsupervised RLVR paradigms attempt to circumvent this by training on pseudo-labels, they are notoriously susceptible to training collapse. Moreover, different samples often exhibit varying annotation values. In this paper, we propose Reinforcement Learning with Active Verifiable Rewards (RLAVR), which actively acquires ground-truth labels for a small set of selected samples and integrates them with pseudo-labels, thereby stabilizing training dynamics and improving performance under limited annotation budgets. To identify valuable samples, we propose the Corrective Advantage Gap (CAG) metric and analyze the sample-level supervision value. Building on this, we introduce Correction-Aware Reliability Estimation for RLAVR (CARE), which translates the oracle CAG criterion into a practical pre-query acquisition policy to substantially improve training stability. Extensive experiments across diverse domains, model families, and model scales demonstrate the effectiveness and generality of our approach. Our code is available at https://github.com/Lumina04/CARE.

Li Wang, Xiaohan Wang, Xiaodong Lu et al.

Large language models (LLMs) have increasingly leveraged tool invocation to enhance their reasoning capabilities. However, existing approaches typically tightly couple tool invocation with immediate execution. Such immediate tool interaction may disrupt the reasoning coherence of LLMs and constrain their expressivity, ultimately degrading reasoning performance. To this end, for the first time, we propose and formalize the problem of decoupling tool invocation from execution during reasoning, and introduce delayed execution with explicit control to enhance tool-integrated reasoning (TIR). Furthermore, we propose a hierarchical control framework and theoretically derive a surrogate loss that enables an implicitly hierarchical policy to learn behavior equivalent to that of an explicit hierarchical policy, leading to the proposed IH-GRPO algorithm. Extensive experiments on IH-GRPO achieve absolute improvements of 1.87\%, 2.16\%, and 2.53\% on Qwen3-1.7B, Qwen3-4B, and Qwen3-8B across six out-of-domain mathematical reasoning benchmarks over the strongest baseline method, while also yielding consistent performance gains in other domains. Our code is available at https://github.com/Lumina04/IH-GRPO-01.

Zihan Lin, Xiaohan Wang, Jie Cao et al.

Reinforcement Learning with Verifiable Rewards (RLVR) enhances reasoning of Large Language Models (LLMs) but usually exhibits limited generation diversity due to the over-incentivization of positive rewards. Although methods like Negative Sample Reinforcement (NSR) mitigate this issue by upweighting penalty from negative samples, they may suppress the semantic distributions shared between positive and negative responses. To boost reasoning ability without losing diversity, this paper proposes negative sample projection Residual Reinforcement Learning (ResRL) that decouples similar semantic distributions among positive and negative responses. We theoretically link Lazy Likelihood Displacement (LLD) to negative-positive head-gradient interference and derive a single-forward proxy that upper-bounds representation alignment to guide conservative advantage reweighting. ResRL then projects negative-token hidden representations onto an SVD-based low-rank positive subspace and uses projection residuals to modulate negative gradients, improving reasoning while preserving diversity and outperforming strong baselines on average across twelve benchmarks spanning Mathematics, Code, Agent Tasks, and Function Calling. Notably, ResRL surpasses NSR on mathematical reasoning by 9.4\% in Avg@16 and 7.0\% in Pass@128. Code is available at https://github.com/1229095296/ResRL.git.

Fengkai Yang, Zherui Chen, Xiaohan Wang et al.

Reinforcement Learning from Verifier Rewards (RLVR) has emerged as a widely used approach for post-training large language models on reasoning tasks, with group-based methods such as GRPO and its variants gaining broad adoption. These methods rely on group-relative advantage estimation to avoid learned critics, yet its theoretical properties remain poorly understood. In this work, we uncover a fundamental issue of group-based RL: the group-relative advantage estimator is inherently biased relative to the true (expected) advantage. We provide the first theoretical analysis showing that it systematically underestimates advantages for hard prompts and overestimates them for easy prompts, leading to imbalanced exploration and exploitation. To address this issue, we propose History-Aware Adaptive Difficulty Weighting (HA-DW), an adaptive reweighting scheme that adjusts advantage estimates based on an evolving difficulty anchor and training dynamics. Both theoretical analysis and experiments on five mathematical reasoning benchmarks demonstrate that HA-DW consistently improves performance when integrated into GRPO and its variants. Our results suggest that correcting biased advantage estimation is critical for robust and efficient RLVR training.

Xiaodong Lu, Xiaohan Wang, Jiajun Chai et al.

Reinforcement Learning with Verifiable Rewards (RLVR) is an effective paradigm for improving the reasoning capabilities of large language models. However, existing RLVR methods utilize rollouts in an indiscriminate and short-horizon manner: responses of heterogeneous quality within each prompt are treated uniformly, and historical rollouts are discarded after a single use. This leads to noisy supervision, poor sample efficiency, and suboptimal policy updates. We address these issues by formulating rollout scheduling in RLVR as a contextual bandit problem and proposing a unified neural scheduling framework that adaptively selects high-value rollouts throughout training. Each rollout is treated as an arm whose reward is defined by the induced performance gain between consecutive optimization steps. The resulting scheduler supports both noise-aware intra-group selection and adaptive global reuse of historical rollouts within a single principled framework. We provide theoretical justification by deriving sublinear regret bounds and showing that enlarging the rollout buffer improves the achievable performance upper bound. Experiments on six mathematical reasoning benchmarks demonstrate consistent gains in performance and training efficiency across multiple RLVR optimization methods.

Xinhao Yang, Zhen Han, Xiaodong Lu et al.

With rapid urbanisation and the accompanying increase in traffic density, traffic noise has become a major concern in urban planning. However, traditional grid noise mapping methods have limitations in terms of time consumption, software costs, and a lack of parameter integration interfaces. These limitations hinder their ability to meet the need for iterative updates and rapid performance feedback in the early design stages of street-scale urban planning. Herein, we developed a rapid urban traffic noise mapping technique that leverages generative adversarial networks (GANs) as a surrogate model. This approach enables the rapid assessment of urban traffic noise distribution by using urban elements such as roads and buildings as the input. The mean values for the mean squared error (RMSE) and structural similarity index (SSIM) are 0.3024 dB(A) and 0.8528, respectively, for the validation dataset. The trained model is integrated into Grasshopper as a tool, facilitating the rapid generation of traffic noise maps. This integration allows urban designers and planners, even those without expertise in acoustics, to easily anticipate changes in acoustics impacts caused by design in the early design stages.