Chengdong Ma

Ruize Zhang, Zelai Xu, Chengdong Ma et al. · tsinghua

Self-play, a learning paradigm where agents iteratively refine their policies by interacting with historical or concurrent versions of themselves or other evolving agents, has shown remarkable success in solving complex non-cooperative multi-agent tasks. Despite its growing prominence in multi-agent reinforcement learning (MARL), such as Go, poker, and video games, a comprehensive and structured understanding of self-play remains lacking. This survey fills this gap by offering a comprehensive roadmap to the diverse landscape of self-play methods. We begin by introducing the necessary preliminaries, including the MARL framework and basic game theory concepts. Then, it provides a unified framework and classifies existing self-play algorithms within this framework. Moreover, the paper bridges the gap between the algorithms and their practical implications by illustrating the role of self-play in different non-cooperative scenarios. Finally, the survey highlights open challenges and future research directions in self-play.

Yali Du, Chengdong Ma, Yuchen Liu et al.

Reinforcement learning algorithms require a large amount of samples; this often limits their real-world applications on even simple tasks. Such a challenge is more outstanding in multi-agent tasks, as each step of operation is more costly requiring communications or shifting or resources. This work aims to improve data efficiency of multi-agent control by model-based learning. We consider networked systems where agents are cooperative and communicate only locally with their neighbors, and propose the decentralized model-based policy optimization framework (DMPO). In our method, each agent learns a dynamic model to predict future states and broadcast their predictions by communication, and then the policies are trained under the model rollouts. To alleviate the bias of model-generated data, we restrain the model usage for generating myopic rollouts, thus reducing the compounding error of model generation. To pertain the independence of policy update, we introduce extended value function and theoretically prove that the resulting policy gradient is a close approximation to true policy gradients. We evaluate our algorithm on several benchmarks for intelligent transportation systems, which are connected autonomous vehicle control tasks (Flow and CACC) and adaptive traffic signal control (ATSC). Empirically results show that our method achieves superior data efficiency and matches the performance of model-free methods using true models.

Chengdong Ma, Ziran Yang, Hai Ci et al.

The primary challenge in deploying Large Language Model (LLM) is ensuring its harmlessness. Red team can identify vulnerabilities by attacking LLM to attain safety. However, current efforts heavily rely on single-round prompt designs and unilateral red team optimizations against fixed blue teams. These static approaches lead to significant reductions in generation diversity, known as the mode collapse, which makes it difficult to discover the potential risks in the increasingly complex human-LLM interactions. Here we introduce dynamic Red Team Game (RTG) to comprehensively analyze the multi-round offensive and defensive interactions between red team and blue team. Furthermore, we develop a Gamified Red Team Solver (GRTS) with diversity measures to mitigate mode collapse and theoretically guarantee the convergence of approximate Nash equilibrium which results in better strategies for both teams. Empirical results demonstrate that GRTS explore diverse and implicit attacks to adaptively exploit various LLMs, surpassing the constraints of specific modes. Insightfully, the geometrical structure we unveil of the red team task aligns with the spinning top hypothesis, confirming the necessity of constructing a diverse LLM population as a promising proxy for heterogeneous human expert red-teamers. This paves the way for scalable toxicity detection and safe alignment for LLMs.

Guangyu Zhao, Ceyao Zhang, Chengdong Ma et al.

Long-horizon tabletop games pose a distinct systems challenge for robotics: small perceptual or execution errors can invalidate accumulated task state, propagate across decision-making modules, and ultimately derail interaction. This paper studies how to maintain internal state consistency in turn-based, multi-human robotic tabletop games through deliberate system design rather than isolated component improvement. Using Mahjong as a representative long-horizon setting, we present an integrated architecture that explicitly maintains perceptual, execution, and interaction state, partitions high-level semantic reasoning from time-critical perception and control, and incorporates verified action primitives with tactile-triggered recovery to prevent premature state corruption. We further introduce interaction-level monitoring mechanisms to detect turn violations and hidden-information breaches that threaten execution assumptions. Beyond demonstrating complete-game operation, we provide an empirical characterization of failure modes, recovery effectiveness, cross-module error propagation, and hardware-algorithm trade-offs observed during deployment. Our results show that explicit partitioning, monitored state transitions, and recovery mechanisms are critical for sustaining executable consistency over extended play, whereas monolithic or unverified pipelines lead to measurable degradation in end-to-end reliability. The proposed system serves as an empirical platform for studying system-level design principles in long-horizon, turn-based interaction.

Haojun Chen, Zili Zou, Chengdong Ma et al.

Reinforcement Learning (RL) offers a powerful paradigm for autonomous robots to master generalist manipulation skills through trial-and-error. However, its real-world application is stifled by severe sample inefficiency. Recent Human-in-the-Loop (HIL) methods accelerate training by using human corrections, yet this approach faces a scalability barrier. Reliance on human supervisors imposes a 1:1 supervision ratio that limits fleet expansion, suffers from operator fatigue over extended sessions, and introduces high variance due to inconsistent human proficiency. We present Agent-guided Policy Search (AGPS), a framework that automates the training pipeline by replacing human supervisors with a multimodal agent. Our key insight is that the agent can be viewed as a semantic world model, injecting intrinsic value priors to structure physical exploration. By using executable tools, the agent provides precise guidance via corrective waypoints and spatial constraints for exploration pruning. We validate our approach on two tasks, ranging from precision insertion to deformable object manipulation. Results demonstrate that AGPS outperforms HIL methods in sample efficiency. This automates the supervision pipeline, unlocking the path to labor-free and scalable robot learning. Project website: https://agps-rl.github.io/agps.

Simin Li, Zihao Mao, Hanxiao Li et al.

In cooperative Multi-Agent Reinforcement Learning (MARL), it is a common practice to tune hyperparameters in ideal simulated environments to maximize cooperative performance. However, policies tuned for cooperation often fail to maintain robustness and resilience under real-world uncertainties. Building trustworthy MARL systems requires a deep understanding of robustness, which ensures stability under uncertainties, and resilience, the ability to recover from disruptions--a concept extensively studied in control systems but largely overlooked in MARL. In this paper, we present a large-scale empirical study comprising over 82,620 experiments to evaluate cooperation, robustness, and resilience in MARL across 4 real-world environments, 13 uncertainty types, and 15 hyperparameters. Our key findings are: (1) Under mild uncertainty, optimizing cooperation improves robustness and resilience, but this link weakens as perturbations intensify. Robustness and resilience also varies by algorithm and uncertainty type. (2) Robustness and resilience do not generalize across uncertainty modalities or agent scopes: policies robust to action noise for all agents may fail under observation noise on a single agent. (3) Hyperparameter tuning is critical for trustworthy MARL: surprisingly, standard practices like parameter sharing, GAE, and PopArt can hurt robustness, while early stopping, high critic learning rates, and Leaky ReLU consistently help. By optimizing hyperparameters only, we observe substantial improvement in cooperation, robustness and resilience across all MARL backbones, with the phenomenon also generalizing to robust MARL methods across these backbones. Code and results available at https://github.com/BUAA-TrustworthyMARL/adv_marl_benchmark .

Yifan Zhong, Chengdong Ma, Xiaoyuan Zhang et al.

Current methods for large language model alignment typically use scalar human preference labels. However, this convention tends to oversimplify the multi-dimensional and heterogeneous nature of human preferences, leading to reduced expressivity and even misalignment. This paper presents Panacea, an innovative approach that reframes alignment as a multi-dimensional preference optimization problem. Panacea trains a single model capable of adapting online and Pareto-optimally to diverse sets of preferences without the need for further tuning. A major challenge here is using a low-dimensional preference vector to guide the model's behavior, despite it being governed by an overwhelmingly large number of parameters. To address this, Panacea is designed to use singular value decomposition (SVD)-based low-rank adaptation, which allows the preference vector to be simply injected online as singular values. Theoretically, we prove that Panacea recovers the entire Pareto front with common loss aggregation methods under mild conditions. Moreover, our experiments demonstrate, for the first time, the feasibility of aligning a single LLM to represent an exponentially vast spectrum of human preferences through various optimization methods. Our work marks a step forward in effectively and efficiently aligning models to diverse and intricate human preferences in a controllable and Pareto-optimal manner.

Zhaowei Zhang, Fengshuo Bai, Qizhi Chen et al.

How to align large language models (LLMs) with user preferences from a static general dataset has been frequently studied. However, user preferences are usually personalized, changing, and diverse regarding culture, values, or time. This leads to the problem that the actual user preferences often do not coincide with those trained by the model developers in the practical use of LLMs. Since we cannot collect enough data and retrain for every demand, researching efficient real-time preference adaptation methods based on the backbone LLMs during test time is important. To this end, we introduce Amulet, a novel, training-free framework that formulates the decoding process of every token as a separate online learning problem with the guidance of simple user-provided prompts, thus enabling real-time optimization to satisfy users' personalized preferences. To reduce the computational cost brought by this optimization process for each token, we additionally provide a closed-form solution for each iteration step of the optimization process, thereby reducing the computational time cost to a negligible level. The detailed experimental results demonstrate that Amulet can achieve significant performance improvements in rich settings with combinations of different LLMs, datasets, and user preferences, while maintaining acceptable computational efficiency.

Mingzhi Wang, Chengdong Ma, Qizhi Chen et al.

Self-play methods have demonstrated remarkable success in enhancing model capabilities across various domains. In the context of Reinforcement Learning from Human Feedback (RLHF), self-play not only boosts Large Language Model (LLM) performance but also overcomes the limitations of traditional Bradley-Terry (BT) model assumptions by finding the Nash equilibrium (NE) of a preference-based, two-player constant-sum game. However, existing methods either guarantee only average-iterate convergence, incurring high storage and inference costs, or converge to the NE of a regularized game, failing to accurately reflect true human preferences. In this paper, we introduce Magnetic Preference Optimization (MPO), a novel approach capable of achieving last-iterate convergence to the NE of the original game, effectively overcoming the limitations of existing methods. Building upon Magnetic Mirror Descent (MMD), MPO attains a linear convergence rate, making it particularly suitable for fine-tuning LLMs. To ensure our algorithm is both theoretically sound and practically viable, we present a simple yet effective implementation that adapts the theoretical insights to the RLHF setting. Empirical results demonstrate that MPO can significantly enhance the performance of LLMs, highlighting the potential of self-play methods in alignment.

Zhaowei Zhang, Fengshuo Bai, Mingzhi Wang et al.

The burgeoning integration of artificial intelligence (AI) into human society brings forth significant implications for societal governance and safety. While considerable strides have been made in addressing AI alignment challenges, existing methodologies primarily focus on technical facets, often neglecting the intricate sociotechnical nature of AI systems, which can lead to a misalignment between the development and deployment contexts. To this end, we posit a new problem worth exploring: Incentive Compatibility Sociotechnical Alignment Problem (ICSAP). We hope this can call for more researchers to explore how to leverage the principles of Incentive Compatibility (IC) from game theory to bridge the gap between technical and societal components to maintain AI consensus with human societies in different contexts. We further discuss three classical game problems for achieving IC: mechanism design, contract theory, and Bayesian persuasion, in addressing the perspectives, potentials, and challenges of solving ICSAP, and provide preliminary implementation conceptions.

Qirui Mi, Qipeng Yang, Zijun Fan et al.

Artificial intelligence (AI) has become a powerful tool for economic research, enabling large-scale simulation and policy optimization. However, applying AI effectively requires simulation platforms for scalable training and evaluation-yet existing environments remain limited to simplified, narrowly scoped tasks, falling short of capturing complex economic challenges such as demographic shifts, multi-government coordination, and large-scale agent interactions. To address this gap, we introduce EconGym, a scalable and modular testbed that connects diverse economic tasks with AI algorithms. Grounded in rigorous economic modeling, EconGym implements 11 heterogeneous role types (e.g., households, firms, banks, governments), their interaction mechanisms, and agent models with well-defined observations, actions, and rewards. Users can flexibly compose economic roles with diverse agent algorithms to simulate rich multi-agent trajectories across 25+ economic tasks for AI-driven policy learning and analysis. Experiments show that EconGym supports diverse and cross-domain tasks-such as coordinating fiscal, pension, and monetary policies-and enables benchmarking across AI, economic methods, and hybrids. Results indicate that richer task composition and algorithm diversity expand the policy space, while AI agents guided by classical economic methods perform best in complex settings. EconGym also scales to 10k agents with high realism and efficiency.

Chengdong Ma, Théo Tao Zhaowei, Pengyu Li et al.

Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a fundamental challenge. This problem represents the local analogue of Hilbert's 18th problem on sphere packing, bridging geometry, number theory, and information theory. Although significant progress has been made through lattices and codes, the irregularities of high-dimensional geometry and exponentially growing combinatorial complexity beyond 8 dimensions, which exceeds the complexity of Go game, limit the scalability of existing methods. Here we model this problem as a two-player matrix completion game and train the game-theoretic reinforcement learning system, PackingStar, to efficiently explore high-dimensional spaces. The matrix entries represent pairwise cosines of sphere center vectors; one player fills entries while another corrects suboptimal ones, jointly maximizing the matrix size, corresponding to the kissing number. This cooperative dynamics substantially improves sample quality, making the extremely large spaces tractable. PackingStar reproduces previous configurations and surpasses all human-known records from dimensions 25 to 31, with the configuration in 25 dimensions geometrically corresponding to the Leech lattice and suggesting possible optimality. It achieves the first breakthrough beyond rational structures from 1971 in 13 dimensions and discovers over 6000 new structures in 14 and other dimensions. These results demonstrate AI's power to explore high-dimensional spaces beyond human intuition and open new pathways for the Kissing Number Problem and broader geometry problems.

Xiaoyuan Zhang, Yizhe Huang, Chengdong Ma et al.

Designing adaptive mechanisms to align individual and collective interests remains a central challenge in artificial social intelligence. Existing methods often struggle with modeling heterogeneous agents possessing persistent latent traits (e.g., skills, preferences) and dealing with complex multi-agent system dynamics. These challenges are compounded by the critical need for high sample efficiency due to costly real-world interactions. World Models, by learning to predict environmental dynamics, offer a promising pathway to enhance mechanism design in heterogeneous and complex systems. In this paper, we introduce a novel method named SWM-AP (Social World Model-Augmented Mechanism Design Policy Learning), which learns a social world model hierarchically modeling agents' behavior to enhance mechanism design. Specifically, the social world model infers agents' traits from their interaction trajectories and learns a trait-based model to predict agents' responses to the deployed mechanisms. The mechanism design policy collects extensive training trajectories by interacting with the social world model, while concurrently inferring agents' traits online during real-world interactions to further boost policy learning efficiency. Experiments in diverse settings (tax policy design, team coordination, and facility location) demonstrate that SWM-AP outperforms established model-based and model-free RL baselines in cumulative rewards and sample efficiency.

Simin Li, Zheng Yuwei, Zihao Mao et al.

Partial agent failure becomes inevitable when systems scale up, making it crucial to identify the subset of agents whose compromise would most severely degrade overall performance. In this paper, we study this Vulnerable Agent Identification (VAI) problem in large-scale multi-agent reinforcement learning (MARL). We frame VAI as a Hierarchical Adversarial Decentralized Mean Field Control (HAD-MFC), where the upper level involves an NP-hard combinatorial task of selecting the most vulnerable agents, and the lower level learns worst-case adversarial policies for these agents using mean-field MARL. The two problems are coupled together, making HAD-MFC difficult to solve. To solve this, we first decouple the hierarchical process by Fenchel-Rockafellar transform, resulting a regularized mean-field Bellman operator for upper level that enables independent learning at each level, thus reducing computational complexity. We then reformulate the upper-level combinatorial problem as a MDP with dense rewards from our regularized mean-field Bellman operator, enabling us to sequentially identify the most vulnerable agents by greedy and RL algorithms. This decomposition provably preserves the optimal solution of the original HAD-MFC. Experiments show our method effectively identifies more vulnerable agents in large-scale MARL and the rule-based system, fooling system into worse failures, and learns a value function that reveals the vulnerability of each agent.

Yan Yu, Yaodong Yang, Zhengbo Lu et al.

Causal inference is crucial for humans to explore the world, which can be modeled to enable an agent to efficiently explore the environment in reinforcement learning. Existing research indicates that establishing the causality between action and state transition will enhance an agent to reason how a policy affects its future trajectory, thereby promoting directed exploration. However, it is challenging to measure the causality due to its intractability in the vast state-action space of complex scenarios. In this paper, we propose a novel Goal Discovery with Causal Capacity (GDCC) framework for efficient environment exploration. Specifically, we first derive a measurement of causality in state space, \emph{i.e.,} causal capacity, which represents the highest influence of an agent's behavior on future trajectories. After that, we present a Monte Carlo based method to identify critical points in discrete state space and further optimize this method for continuous high-dimensional environments. Those critical points are used to uncover where the agent makes important decisions in the environment, which are then regarded as our subgoals to guide the agent to make exploration more purposefully and efficiently. Empirical results from multi-objective tasks demonstrate that states with high causal capacity align with our expected subgoals, and our GDCC achieves significant success rate improvements compared to baselines.

Qirui Mi, Zhiyu Zhao, Chengdong Ma et al.

Macroeconomic outcomes emerge from individuals' decisions, making it essential to model how agents interact with macro policy via consumption, investment, and labor choices. We formulate this as a dynamic Stackelberg game: the government (leader) sets policies, and agents (followers) respond by optimizing their behavior over time. Unlike static models, this dynamic formulation captures temporal dependencies and strategic feedback critical to policy design. However, as the number of agents increases, explicitly simulating all agent-agent and agent-government interactions becomes computationally infeasible. To address this, we propose the Dynamic Stackelberg Mean Field Game (DSMFG) framework, which approximates these complex interactions via agent-population and government-population couplings. This approximation preserves individual-level feedback while ensuring scalability, enabling DSMFG to jointly model three core features of real-world policymaking: dynamic feedback, asymmetry, and large scale. We further introduce Stackelberg Mean Field Reinforcement Learning (SMFRL), a data-driven algorithm that learns the leader's optimal policies while maintaining personalized responses for individual agents. Empirically, we validate our approach in a large-scale simulated economy, where it scales to 1,000 agents (vs. 100 in prior work) and achieves a fourfold increase in GDP over classical economic methods and a nineteenfold improvement over the static 2022 U.S. federal income tax policy.

Yaodong Yang, Chengdong Ma, Zihan Ding et al.

Tremendous advances have been made in multiagent reinforcement learning (MARL). MARL corresponds to the learning problem in a multiagent system in which multiple agents learn simultaneously. It is an interdisciplinary field of study with a long history that includes game theory, machine learning, stochastic control, psychology, and optimization. Despite great successes in MARL, there is a lack of a self-contained overview of the literature that covers game-theoretic foundations of modern MARL methods and summarizes the recent advances. The majority of existing surveys are outdated and do not fully cover the recent developments since 2010. In this work, we provide a monograph on MARL that covers both the fundamentals and the latest developments on the research frontier. The goal of this monograph is to provide a self-contained assessment of the current state-of-the-art MARL techniques from a game-theoretic perspective. We expect this work to serve as a stepping stone for both new researchers who are about to enter this fast-growing field and experts in the field who want to obtain a panoramic view and identify new directions based on recent advances.