Organizations: Shanghai Jiao Tong University · Shanghai AI Laboratory · Shandong University
Abstract
Post-training has significantly enhanced the reasoning capability of Large Reasoning Models (LRMs), especially with Reinforcement Learning (RL) like Group Relative Policy Optimization (GRPO). However, GRPO-style RL methods in multi-domain settings often fail to achieve consistent improvements across all domains due to inherent interference in policy optimization. Prior studies on multi-domain RL primarily focus on alleviating cross-domain interference, while often neglecting the pivotal role of knowledge sharing, which we argue is the key to transforming cross-domain interactions from harmful competition into beneficial transfer. To address this limitation, we propose Multi-domain Contrastive Policy Optimization (MCPO), which analyzes the structural relationships among rollouts and promotes cross-domain knowledge sharing and in-domain knowledge consolidation in a contrastive manner. Specifically, for a given prompt, MCPO identifies transferable reasoning trajectories from other domains as positive examples, while treating incorrect rollouts as negative ones. It then encourages consistent representations for positive pairs and pushes negative pairs apart, thereby facilitating knowledge transfer and reducing interference. Moreover, MCPO aligns intra-domain correct rollouts to build a consolidated representation space. In this way, MCPO contrastively learns a harmonious representation space that can accommodate diverse multi-domain knowledge. Empirical results show that MCPO improves the reasoning capabilities of LRMs across multiple domains and even outperforms single-domain training in some cases. Code is available at https://github.com/Maricalce/MCPO.
Reinforcement Learning with Verifiable Rewards (RLVR) plays a key role in stimulating the explicit reasoning capability of Large Language Models (LLMs). We can achieve expert-level performance in some specific domains via RLVR, such as coding or math. When a general multi-domain expert-level model is required, we need to carefully consider the collaboration of RLVR across different domains. The current state-of-the-art models mainly employ two different training paradigms for multi-domain RLVR: mixed multi-task RLVR and separate RLVR followed by model merging. However, most of the works did not provide a detailed comparison and analysis about these paradigms. To this end, we choose multiple commonly used high-level tasks (e.g., math, coding, science, instruction following, and agent) as our target domains and design extensive qualitative and quantitative experiments using open-source datasets. We find the RLVR across domains exhibits small mutual interferences, and reasoning-intensive domains have mutually synergistic effects. Furthermore, we analyze the internal mechanisms from the perspectives of information constraints, model prediction behavior and self-verification. Our homepage is at https://github.com/Mosi-AI/M2RL.
Reinforcement learning with verifiers (RLVR) has become a central paradigm for improving LLM reasoning, yet popular group-based optimization algorithms like GRPO often suffer from exploration collapse, where the models prematurely converge on a narrow set of high-scoring patterns, lacking the ability to explore new solutions. Recent efforts attempt to alleviate this by adding entropy regularization or diversity bonus. However, these approaches do not change the \textit{winner-takes-all} nature, where rollouts still compete for individual advantage rather than cooperating for maximizing global diversity. In this work, we propose Group Cooperative Policy Optimization (GCPO), which shifts the training paradigm from rollout competition to team cooperation. Specifically, GCPO replaces independent rollout scoring with team-level credit assignment: a rollout is rewarded by how much it contributes to the team's valid solution coverage, rather than its individual accuracy. This coverage is described as a determinant volume over reward-weighted semantic embeddings, where only correct and non-redundant rollouts contribute to this volume. During advantage estimation, GCPO redistributes the collective team reward to each single rollout according to its average marginal contribution to the team. This cooperative training paradigm routes optimization toward non-redundant correct reasoning paths. Experiments across multiple reasoning benchmarks demonstrate that GCPO significantly improves both reasoning accuracy and solution diversity over existing approaches. Code will be released at https://github.com/bradybuddiemarch/gcpo.
Existing reinforcement learning approaches for Large Language Models typically perform policy optimization at the granularity of individual tokens or entire response sequences. However, such formulations often misalign with the natural step-wise structure of reasoning processes, leading to suboptimal credit assignment and unstable training in multi-modal reasoning tasks. To bridge this gap, we propose Segment-Aligned Policy Optimization (SAPO), a novel reinforcement learning paradigm that treats coherent reasoning steps, rather than tokens or full sequences as fundamental units of policy update. SAPO introduces a step-wise Markov decision process abstraction over reasoning segments, accompanied by segment-level value estimation, advantage computation, and importance sampling mechanisms that are semantically aligned with reasoning boundaries. Experiments on representative reasoning benchmarks demonstrate that SAPO consistently outperforms token-level and sequence-level policy optimization methods, achieving significant accuracy improvements while exhibiting better training stability and value estimation consistency. Our work underscores the importance of aligning reinforcement learning updates with the intrinsic structure of reasoning, paving the way for more efficient and semantically grounded policy optimization in complex reasoning tasks. Codes and models will be released to ensure full reproducibility.