Yuanheng Zhu

Zijie Zhao, Honglei Guo, Shengqian Chen et al.

Model-based reinforcement learning (MBRL) has achieved remarkable success in robotics due to its high sample efficiency and planning capability. However, extending MBRL to physical multi-robot cooperation remains challenging due to the complexity of joint dynamics. To address this challenge, we propose the Sequential World Model (SeqWM), a novel framework that integrates the sequential paradigm into multi-robot MBRL. SeqWM employs independent, autoregressive agent-wise world models to represent joint dynamics, where each agent generates its future trajectory and plans its actions based on the predictions of its predecessors. This design lowers modeling complexity and enables the emergence of advanced cooperative behaviors through explicit intention sharing. Experiments on Bi-DexHands and Multi-Quadruped demonstrate that SeqWM outperforms existing state-of-the-art model-based and model-free baselines in both overall performance and sample efficiency, while exhibiting advanced cooperative behaviors such as predictive adaptation, temporal alignment, and role division. Furthermore, SeqWM has been successfully deployed on physical quadruped robots, validating its effectiveness in real-world multi-robot systems. Demos and code are available at: https://github.com/zhaozijie2022/seqwm

Jiajun Chai, Wenzhang Chen, Yuanheng Zhu et al.

Unmanned combat air vehicle (UCAV) combat is a challenging scenario with continuous action space. In this paper, we propose a general hierarchical framework to resolve the within-vision-range (WVR) air-to-air combat problem under 6 dimensions of degree (6-DOF) dynamics. The core idea is to divide the whole decision process into two loops and use reinforcement learning (RL) to solve them separately. The outer loop takes into account the current combat situation and decides the expected macro behavior of the aircraft according to a combat strategy. Then the inner loop tracks the macro behavior with a flight controller by calculating the actual input signals for the aircraft. We design the Markov decision process for both the outer loop strategy and inner loop controller, and train them by proximal policy optimization (PPO) algorithm. For the inner loop controller, we design an effective reward function to accurately track various macro behavior. For the outer loop strategy, we further adopt a fictitious self-play mechanism to improve the combat performance by constantly combating against the historical strategies. Experiment results show that the inner loop controller can achieve better tracking performance than fine-tuned PID controller, and the outer loop strategy can perform complex maneuvers to get higher and higher winning rate, with the generation evolves.

Yuqian Fu, Haohuan Huang, Kaiwen Jiang et al.

On-policy distillation (OPD) is appealing for large language model (LLM) post-training because it evaluates teacher feedback on student-generated rollouts rather than fixed teacher traces. In long-horizon settings, however, the common sampled-token variant is fragile: it reduces distribution matching to a one-token signal and becomes increasingly unreliable as rollouts drift away from prefixes the teacher commonly visits. We revisit OPD from the estimator and implementation sides. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL, but it has a much tighter worst-case variance bound; our toy study shows the same tradeoff empirically, with stronger future-reward coupling producing higher gradient variance and less stable learning. Empirically, we identify three failure modes of sampled-token OPD: an imbalanced one-token signal, unreliable teacher guidance on student-generated prefixes, and distortions caused by tokenizer or special-token mismatch. We address these issues with teacher top-K local support matching, implemented as truncated reverse-KL with top-p rollout sampling and special-token masking. Across single-task math reasoning and multi-task agentic-plus-math training, this objective yields more stable optimization and better downstream performance than sampled-token OPD.

Yaocheng Zhang, Jiajun Chai, Songjun Tu et al.

On-policy distillation (OPD) provides dense teacher feedback along rollouts generated by the student and has emerged as a promising post-training paradigm for long-horizon reasoning. However, standard OPD typically generates full rollouts during training, which is computationally expensive and may expose the student to unreliable teacher feedback at late rollout positions, especially during early training. We identify the rollout horizon as a key bottleneck in OPD that substantially impacts training efficiency. Unlike Reinforcement Learning with Verifiable Rewards (RLVR), OPD does not require a complete trajectory or a final answer reward to provide learning signals. This observation suggests that full rollouts may not always be necessary for effective OPD. Motivated by this insight, we propose two simple horizon-control strategies: Progressive OPD (POPD), which gradually expands the rollout horizon during training, and Truncated OPD (TOPD), which permanently performs distillation on reliable truncated rollouts. Experiments on mathematical reasoning show that POPD improves the training efficiency of OPD by up to 3$\times$, while TOPD matches OPD performance using only 10\% of the rollout horizon, leading to substantial wall-clock and memory reductions. These results demonstrate that controlling the rollout horizon offers a simple and practical path to more efficient OPD.

Yaocheng Zhang, Yuanheng Zhu, Wenyue Chong et al.

Deep search agents have emerged as a promising paradigm for addressing complex information-seeking tasks, but their training remains challenging due to sparse rewards, weak credit assignment, and limited labeled data. Self-play offers a scalable route to reduce data dependence, but conventional self-play optimizes students only through sparse outcome rewards, leading to low learning efficiency. In this work, we observe that self-play naturally produces a question construction path (QCP) during task generation, an intermediate artifact that captures the reverse solution process. This reveals a new source of privileged information for self-distillation: self-play can itself provide high-quality privileged context for the teacher model in a low-cost and scalable manner, without relying on human feedback or curated privileged information. Leveraging this insight, we propose Privileged Information Self-Play ($π$-Play), a multi-agent self-evolution framework. In $π$-Play, an examiner generates tasks together with their QCPs, and a teacher model leverages QCP as privileged context to densely supervise a student via self-distillation. This design transforms conventional sparse-reward self-play into a dense-feedback self-evolution loop. Extensive experiments show that data-free $π$-Play surpasses fully supervised search agents and improves evolutionary efficiency by 2-3$\times$ over conventional self-play.

Runyu Lu, Peng Zhang, Ruochuan Shi et al.

Equilibrium learning in adversarial games is an important topic widely examined in the fields of game theory and reinforcement learning (RL). Pursuit-evasion game (PEG), as an important class of real-world games from the fields of robotics and security, requires exponential time to be accurately solved. When the underlying graph structure varies, even the state-of-the-art RL methods require recomputation or at least fine-tuning, which can be time-consuming and impair real-time applicability. This paper proposes an Equilibrium Policy Generalization (EPG) framework to effectively learn a generalized policy with robust cross-graph zero-shot performance. In the context of PEGs, our framework is generally applicable to both pursuer and evader sides in both no-exit and multi-exit scenarios. These two generalizability properties, to our knowledge, are the first to appear in this domain. The core idea of the EPG framework is to train an RL policy across different graph structures against the equilibrium policy for each single graph. To construct an equilibrium oracle for single-graph policies, we present a dynamic programming (DP) algorithm that provably generates pure-strategy Nash equilibrium with near-optimal time complexity. To guarantee scalability with respect to pursuer number, we further extend DP and RL by designing a grouping mechanism and a sequence model for joint policy decomposition, respectively. Experimental results show that, using equilibrium guidance and a distance feature proposed for cross-graph PEG training, the EPG framework guarantees desirable zero-shot performance in various unseen real-world graphs. Besides, when trained under an equilibrium heuristic proposed for the graphs with exits, our generalized pursuer policy can even match the performance of the fine-tuned policies from the state-of-the-art PEG methods.

Yuanyang Zhu, Zhi Wang, Yuanheng Zhu et al.

For on-policy reinforcement learning, discretizing action space for continuous control can easily express multiple modes and is straightforward to optimize. However, without considering the inherent ordering between the discrete atomic actions, the explosion in the number of discrete actions can possess undesired properties and induce a higher variance for the policy gradient estimator. In this paper, we introduce a straightforward architecture that addresses this issue by constraining the discrete policy to be unimodal using Poisson probability distributions. This unimodal architecture can better leverage the continuity in the underlying continuous action space using explicit unimodal probability distributions. We conduct extensive experiments to show that the discrete policy with the unimodal probability distribution provides significantly faster convergence and higher performance for on-policy reinforcement learning algorithms in challenging control tasks, especially in highly complex tasks such as Humanoid. We provide theoretical analysis on the variance of the policy gradient estimator, which suggests that our attentively designed unimodal discrete policy can retain a lower variance and yield a stable learning process.

Yaocheng Zhang, Haohuan Huang, Zijun Song et al.

Tool-Integrated Reasoning (TIR) with search engines enables large language models to iteratively retrieve up-to-date external knowledge, enhancing adaptability and generalization in complex question-answering tasks. However, existing search agent pipelines typically depend on reinforcement learning based optimization, which often suffers from sparse outcome rewards, leading to inefficient exploration and unstable training. We introduce CriticSearch, a fine-grained credit-assignment framework that supplies dense, turn-level feedback via a retrospective critic mechanism. During training, a frozen, asymmetric critique LLM retrospectively evaluates each turn using privileged information from the full trajectory and gold answers, converting these assessments into stable, dense rewards that guide policy improvement. Experimental results across diverse multi-hop reasoning benchmarks demonstrate that CriticSearch consistently outperforms existing baselines, achieving faster convergence, improved training stability, and higher performance.

Ruochuan Shi, Runyu Lu, Yuanheng Zhu et al.

In graph-structured multi-agent reinforcement learning (MARL) adversarial tasks such as pursuit and confrontation, agents must coordinate under highly dynamic interactions, where sparse rewards hinder efficient policy learning. We propose Adaptive Regularized Multi-Agent Soft Actor-Critic (ARAC), which integrates an attention-based graph neural network (GNN) for modeling agent dependencies with an adaptive divergence regularization mechanism. The GNN enables expressive representation of spatial relations and state features in graph environments. Divergence regularization can serve as policy guidance to alleviate the sparse reward problem, but it may lead to suboptimal convergence when the reference policy itself is imperfect. The adaptive divergence regularization mechanism enables the framework to exploit reference policies for efficient exploration in the early stages, while gradually reducing reliance on them as training progresses to avoid inheriting their limitations. Experiments in pursuit and confrontation scenarios demonstrate that ARAC achieves faster convergence, higher final success rates, and stronger scalability across varying numbers of agents compared with MARL baselines, highlighting its effectiveness in complex graph-structured environments.

Zhi Wang, Li Zhang, Wenhao Wu et al.

A longstanding goal of artificial general intelligence is highly capable generalists that can learn from diverse experiences and generalize to unseen tasks. The language and vision communities have seen remarkable progress toward this trend by scaling up transformer-based models trained on massive datasets, while reinforcement learning (RL) agents still suffer from poor generalization capacity under such paradigms. To tackle this challenge, we propose Meta Decision Transformer (Meta-DT), which leverages the sequential modeling ability of the transformer architecture and robust task representation learning via world model disentanglement to achieve efficient generalization in offline meta-RL. We pretrain a context-aware world model to learn a compact task representation, and inject it as a contextual condition to the causal transformer to guide task-oriented sequence generation. Then, we subtly utilize history trajectories generated by the meta-policy as a self-guided prompt to exploit the architectural inductive bias. We select the trajectory segment that yields the largest prediction error on the pretrained world model to construct the prompt, aiming to encode task-specific information complementary to the world model maximally. Notably, the proposed framework eliminates the requirement of any expert demonstration or domain knowledge at test time. Experimental results on MuJoCo and Meta-World benchmarks across various dataset types show that Meta-DT exhibits superior few and zero-shot generalization capacity compared to strong baselines while being more practical with fewer prerequisites. Our code is available at https://github.com/NJU-RL/Meta-DT.

Yuqian Fu, Tinghong Chen, Jiajun Chai et al.

Large language models (LLMs) have achieved remarkable progress in reasoning tasks, yet the optimal integration of Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) remains a fundamental challenge. Through comprehensive analysis of token distributions, learning dynamics, and integration mechanisms from entropy-based perspectives, we reveal key differences between these paradigms: SFT induces coarse-grained global changes to LLM policy distributions, while RL performs fine-grained selective optimizations, with entropy serving as a critical indicator of training effectiveness. Building on these observations, we propose Supervised Reinforcement Fine-Tuning (SRFT), a single-stage method that unifies both fine-tuning paradigms through entropy-aware weighting mechanisms. Our approach simultaneously applies SFT and RL to directly optimize the LLM using demonstrations and self-exploration rollouts rather than through two-stage sequential methods. Extensive experiments show that SRFT achieves 59.1% average accuracy, outperforming zero-RL methods by 9.0% on five mathematical reasoning benchmarks and 10.9% on three out-of-distribution benchmarks.

Yuqian Fu, Yuanheng Zhu, Jiajun Chai et al.

Ensembling large language models (LLMs) can effectively combine diverse strengths of different models, offering a promising approach to enhance performance across various tasks. However, existing methods typically rely on fixed weighting strategies that fail to adapt to the dynamic, context-dependent characteristics of LLM capabilities. In this work, we propose Reinforcement Learning-Assisted Ensemble for LLMs (RLAE), a novel framework that reformulates LLM ensemble through the lens of a Markov Decision Process (MDP). Our approach introduces a RL agent that dynamically adjusts ensemble weights by considering both input context and intermediate generation states, with the agent being trained using rewards that directly correspond to the quality of final outputs. We implement RLAE using both single-agent and multi-agent reinforcement learning algorithms ($\text{RLAE}_\text{PPO}$ and $\text{RLAE}_\text{MAPPO}$ ), demonstrating substantial improvements over conventional ensemble methods. Extensive evaluations on a diverse set of tasks show that RLAE outperforms existing approaches by up to $3.3\%$ accuracy points, offering a more effective framework for LLM ensembling. Furthermore, our method exhibits superior generalization capabilities across different tasks without the need for retraining, while simultaneously achieving lower time latency.

Guangzheng Hu, Yuanheng Zhu, Haoran Li et al.

Many real-world applications involve some agents that fall into two teams, with payoffs that are equal within the same team but of opposite sign across the opponent team. The so-called two-team zero-sum Markov games (2t0sMGs) can be resolved with reinforcement learning in recent years. However, existing methods are thus inefficient in light of insufficient consideration of intra-team credit assignment, data utilization and computational intractability. In this paper, we propose the individual-global-minimax (IGMM) principle to ensure the coherence between two-team minimax behaviors and the individual greedy behaviors through Q functions in 2t0sMGs. Based on it, we present a novel multi-agent reinforcement learning framework, Factorized Multi-Agent MiniMax Q-Learning (FM3Q), which can factorize the joint minimax Q function into individual ones and iteratively solve for the IGMM-satisfied minimax Q functions for 2t0sMGs. Moreover, an online learning algorithm with neural networks is proposed to implement FM3Q and obtain the deterministic and decentralized minimax policies for two-team players. A theoretical analysis is provided to prove the convergence of FM3Q. Empirically, we use three environments to evaluate the learning efficiency and final performance of FM3Q and show its superiority on 2t0sMGs.

Kaixuan Xu, Jiajun Chai, Sicheng Li et al.

Diplomacy is a complex multiplayer game that requires both cooperation and competition, posing significant challenges for AI systems. Traditional methods rely on equilibrium search to generate extensive game data for training, which demands substantial computational resources. Large Language Models (LLMs) offer a promising alternative, leveraging pre-trained knowledge to achieve strong performance with relatively small-scale fine-tuning. However, applying LLMs to Diplomacy remains challenging due to the exponential growth of possible action combinations and the intricate strategic interactions among players. To address this challenge, we propose DipLLM, a fine-tuned LLM-based agent that learns equilibrium policies for Diplomacy. DipLLM employs an autoregressive factorization framework to simplify the complex task of multi-unit action assignment into a sequence of unit-level decisions. By defining an equilibrium policy within this framework as the learning objective, we fine-tune the model using only 1.5% of the data required by the state-of-the-art Cicero model, surpassing its performance. Our results demonstrate the potential of fine-tuned LLMs for tackling complex strategic decision-making in multiplayer games.

Runyu Lu, Ruochuan Shi, Yuanheng Zhu et al.

Computing worst-case robust strategies in pursuit-evasion games (PEGs) is time-consuming, especially when real-world factors like partial observability are considered. While important for general security purposes, real-time applicable pursuit strategies for graph-based PEGs are currently missing when the pursuers only have imperfect information about the evader's position. Although state-of-the-art reinforcement learning (RL) methods like Equilibrium Policy Generalization (EPG) and Grasper provide guidelines for learning graph neural network (GNN) policies robust to different game dynamics, they are restricted to the scenario of perfect information and do not take into account the possible case where the evader can predict the pursuers' actions. This paper introduces the first approach to worst-case robust real-time pursuit strategies (R2PS) under partial observability. We first prove that a traditional dynamic programming (DP) algorithm for solving Markov PEGs maintains optimality under the asynchronous moves by the evader. Then, we propose a belief preservation mechanism about the evader's possible positions, extending the DP pursuit strategies to a partially observable setting. Finally, we embed the belief preservation into the state-of-the-art EPG framework to finish our R2PS learning scheme, which leads to a real-time pursuer policy through cross-graph reinforcement learning against the asynchronous-move DP evasion strategies. After reinforcement learning, our policy achieves robust zero-shot generalization to unseen real-world graph structures and consistently outperforms the policy directly trained on the test graphs by the existing game RL approach.

Zhentao Tang, Yuanheng Zhu, Dongbin Zhao et al.

The Fighting Game AI Competition (FTGAIC) provides a challenging benchmark for 2-player video game AI. The challenge arises from the large action space, diverse styles of characters and abilities, and the real-time nature of the game. In this paper, we propose a novel algorithm that combines Rolling Horizon Evolution Algorithm (RHEA) with opponent model learning. The approach is readily applicable to any 2-player video game. In contrast to conventional RHEA, an opponent model is proposed and is optimized by supervised learning with cross-entropy and reinforcement learning with policy gradient and Q-learning respectively, based on history observations from opponent. The model is learned during the live gameplay. With the learned opponent model, the extended RHEA is able to make more realistic plans based on what the opponent is likely to do. This tends to lead to better results. We compared our approach directly with the bots from the FTGAIC 2018 competition, and found our method to significantly outperform all of them, for all three character. Furthermore, our proposed bot with the policy-gradient-based opponent model is the only one without using Monte-Carlo Tree Search (MCTS) among top five bots in the 2019 competition in which it achieved second place, while using much less domain knowledge than the winner.

Kun Shao, Zhentao Tang, Yuanheng Zhu et al.

Deep reinforcement learning (DRL) has made great achievements since proposed. Generally, DRL agents receive high-dimensional inputs at each step, and make actions according to deep-neural-network-based policies. This learning mechanism updates the policy to maximize the return with an end-to-end method. In this paper, we survey the progress of DRL methods, including value-based, policy gradient, and model-based algorithms, and compare their main techniques and properties. Besides, DRL plays an important role in game artificial intelligence (AI). We also take a review of the achievements of DRL in various video games, including classical Arcade games, first-person perspective games and multi-agent real-time strategy games, from 2D to 3D, and from single-agent to multi-agent. A large number of video game AIs with DRL have achieved super-human performance, while there are still some challenges in this domain. Therefore, we also discuss some key points when applying DRL methods to this field, including exploration-exploitation, sample efficiency, generalization and transfer, multi-agent learning, imperfect information, and delayed spare rewards, as well as some research directions.

Kun Shao, Yuanheng Zhu, Dongbin Zhao

Real-time strategy games have been an important field of game artificial intelligence in recent years. This paper presents a reinforcement learning and curriculum transfer learning method to control multiple units in StarCraft micromanagement. We define an efficient state representation, which breaks down the complexity caused by the large state space in the game environment. Then a parameter sharing multi-agent gradientdescent Sarsa(λ) (PS-MAGDS) algorithm is proposed to train the units. The learning policy is shared among our units to encourage cooperative behaviors. We use a neural network as a function approximator to estimate the action-value function, and propose a reward function to help units balance their move and attack. In addition, a transfer learning method is used to extend our model to more difficult scenarios, which accelerates the training process and improves the learning performance. In small scale scenarios, our units successfully learn to combat and defeat the built-in AI with 100% win rates. In large scale scenarios, curriculum transfer learning method is used to progressively train a group of units, and shows superior performance over some baseline methods in target scenarios. With reinforcement learning and curriculum transfer learning, our units are able to learn appropriate strategies in StarCraft micromanagement scenarios.