Zongkai Liu

Fanqing Meng, Lingxiao Du, Zongkai Liu et al.

DeepSeek R1, and o1 have demonstrated powerful reasoning capabilities in the text domain through stable large-scale reinforcement learning. To enable broader applications, some works have attempted to transfer these capabilities to multimodal reasoning. However, these efforts have been limited by the limited difficulty of selected tasks and relatively small training scales, making it challenging to demonstrate strong multimodal reasoning abilities. To address this gap, we introduce the MMK12 dataset and MM-EUREKA with 7B and 32B parameters. The former is a high-quality multimodal mathematics reasoning dataset featuring diverse knowledge domains with human-verified answers and solution processes. The latter is a multimodal model employing rule-based reinforcement learning on MMK12, utilizing online filtering and two-stage training strategy to enhance training stability. MM-EUREKA demonstrates remarkable performance gains in multimodal mathematical reasoning, outperforming previous powerful models like InternVL2.5-78B or InternVL2.5-38B-MPO. In particular, MM-EUREKA achieves competitive or superior performance compared to both open-source and closed-source models, and trails slightly behind o1 in multidisciplinary reasoning tasks. We open-source our complete pipeline to foster further research in this area. We release all our codes, models, data, etc. at https://github.com/ModalMinds/MM-EUREKA

Lingxiao Du, Fanqing Meng, Zongkai Liu et al.

While Multimodal Large Language Models (MLLMs) have achieved impressive progress in vision-language understanding, they still struggle with complex multi-step reasoning, often producing logically inconsistent or partially correct solutions. A key limitation lies in the lack of fine-grained supervision over intermediate reasoning steps. To address this, we propose MM-PRM, a process reward model trained within a fully automated, scalable framework. We first build MM-Policy, a strong multimodal model trained on diverse mathematical reasoning data. Then, we construct MM-K12, a curated dataset of 10,000 multimodal math problems with verifiable answers, which serves as seed data. Leveraging a Monte Carlo Tree Search (MCTS)-based pipeline, we generate over 700k step-level annotations without human labeling. The resulting PRM is used to score candidate reasoning paths in the Best-of-N inference setup and achieves significant improvements across both in-domain (MM-K12 test set) and out-of-domain (OlympiadBench, MathVista, etc.) benchmarks. Further analysis confirms the effectiveness of soft labels, smaller learning rates, and path diversity in optimizing PRM performance. MM-PRM demonstrates that process supervision is a powerful tool for enhancing the logical robustness of multimodal reasoning systems. We release all our codes and data at https://github.com/ModalMinds/MM-PRM.

Zongkai Liu, Fanqing Meng, Lingxiao Du et al.

Recent advances in rule-based reinforcement learning (RL) have significantly improved the reasoning capability of language models (LMs) with rule-based rewards. However, existing RL methods -- such as GRPO, REINFORCE++, and RLOO -- often suffer from training instability, where large policy updates and improper clipping can lead to training collapse. To address this issue, we propose Clipped Policy Gradient Optimization with Policy Drift (CPGD), a novel algorithm designed to stabilize policy learning in LMs. CPGD introduces a policy drift constraint based on KL divergence to dynamically regularize policy updates, and leverages a clip mechanism on the logarithm of the ratio to prevent excessive policy updates. We provide theoretical justification for CPGD and demonstrate through empirical analysis that it mitigates the instability observed in prior approaches. Furthermore, we show that CPGD significantly improves performance while maintaining training stability. Our implementation balances theoretical rigor with practical usability, offering a robust alternative for RL in the post-training of LMs. We release our code at https://github.com/ModalMinds/MM-EUREKA.

Qian Lin, Zongkai Liu, Danying Mo et al.

In recent years, significant progress has been made in multi-objective reinforcement learning (RL) research, which aims to balance multiple objectives by incorporating preferences for each objective. In most existing studies, specific preferences must be provided during deployment to indicate the desired policies explicitly. However, designing these preferences depends heavily on human prior knowledge, which is typically obtained through extensive observation of high-performing demonstrations with expected behaviors. In this work, we propose a simple yet effective offline adaptation framework for multi-objective RL problems without assuming handcrafted target preferences, but only given several demonstrations to implicitly indicate the preferences of expected policies. Additionally, we demonstrate that our framework can naturally be extended to meet constraints on safety-critical objectives by utilizing safe demonstrations, even when the safety thresholds are unknown. Empirical results on offline multi-objective and safe tasks demonstrate the capability of our framework to infer policies that align with real preferences while meeting the constraints implied by the provided demonstrations.

Qian Lin, Chao Yu, Zongkai Liu et al.

In this paper, we aim to utilize only offline trajectory data to train a policy for multi-objective RL. We extend the offline policy-regularized method, a widely-adopted approach for single-objective offline RL problems, into the multi-objective setting in order to achieve the above goal. However, such methods face a new challenge in offline MORL settings, namely the preference-inconsistent demonstration problem. We propose two solutions to this problem: 1) filtering out preference-inconsistent demonstrations via approximating behavior preferences, and 2) adopting regularization techniques with high policy expressiveness. Moreover, we integrate the preference-conditioned scalarized update method into policy-regularized offline RL, in order to simultaneously learn a set of policies using a single policy network, thus reducing the computational cost induced by the training of a large number of individual policies for various preferences. Finally, we introduce Regularization Weight Adaptation to dynamically determine appropriate regularization weights for arbitrary target preferences during deployment. Empirical results on various multi-objective datasets demonstrate the capability of our approach in solving offline MORL problems.

Zongkai Liu, Qian Lin, Chao Yu et al.

Offline Multi-Agent Reinforcement Learning (MARL) is an emerging field that aims to learn optimal multi-agent policies from pre-collected datasets. Compared to single-agent case, multi-agent setting involves a large joint state-action space and coupled behaviors of multiple agents, which bring extra complexity to offline policy optimization. In this work, we revisit the existing offline MARL methods and show that in certain scenarios they can be problematic, leading to uncoordinated behaviors and out-of-distribution (OOD) joint actions. To address these issues, we propose a new offline MARL algorithm, named In-Sample Sequential Policy Optimization (InSPO). InSPO sequentially updates each agent's policy in an in-sample manner, which not only avoids selecting OOD joint actions but also carefully considers teammates' updated policies to enhance coordination. Additionally, by thoroughly exploring low-probability actions in the behavior policy, InSPO can well address the issue of premature convergence to sub-optimal solutions. Theoretically, we prove InSPO guarantees monotonic policy improvement and converges to quantal response equilibrium (QRE). Experimental results demonstrate the effectiveness of our method compared to current state-of-the-art offline MARL methods.