Shengbo Eben Li

Zuxing Lu, Ziang Zheng, Yao Lyu et al.

Building a general-purpose whole-body controller is essential for enabling diverse motion capabilities in humanoid robots across a wide range of downstream tasks, including locomotion and loco-manipulation. Different tasks rely on distinct motion reference modalities: locomotion primarily depends on coordinated robot joint trajectories, whereas manipulation requires precise end-effector trajectory tracking. Existing methods often overlook the representational mismatch between dense robot joint angles and sparse end-effector poses. To address this, we propose Multi-Modal Mimic (M3imic), a versatile multi-modal whole-body control framework that unifies heterogeneous motion reference modalities, including robot joint angles, human pose trajectories, and end-effector poses, using modality-specific encoders to map them into a shared latent space. Leveraging large-scale reinforcement learning in the simulator, we train a single policy that achieves sim-to-real transfer across multiple motion reference modalities without modality-specific retraining. Extensive simulation and real-world experiments on the Unitree G1 robot are conducted to evaluate the proposed framework. In simulation, the policy achieves a peak success rate of 98.42\% on an unseen test dataset, demonstrating its exceptional generalization capability. The code is available at https://github.com/Renforce-Dynamics/MultiModalWBC

Hao Sha, Yao Mu, Yuxuan Jiang et al.

Existing learning-based autonomous driving (AD) systems face challenges in comprehending high-level information, generalizing to rare events, and providing interpretability. To address these problems, this work employs Large Language Models (LLMs) as a decision-making component for complex AD scenarios that require human commonsense understanding. We devise cognitive pathways to enable comprehensive reasoning with LLMs, and develop algorithms for translating LLM decisions into actionable driving commands. Through this approach, LLM decisions are seamlessly integrated with low-level controllers by guided parameter matrix adaptation. Extensive experiments demonstrate that our proposed method not only consistently surpasses baseline approaches in single-vehicle tasks, but also helps handle complex driving behaviors even multi-vehicle coordination, thanks to the commonsense reasoning capabilities of LLMs. This paper presents an initial step toward leveraging LLMs as effective decision-makers for intricate AD scenarios in terms of safety, efficiency, generalizability, and interoperability. We aspire for it to serve as inspiration for future research in this field. Project page: https://sites.google.com/view/llm-mpc

Zhitao Wang, Yang Zheng, Shengbo Eben Li et al.

This paper proposes a parallel optimization algorithm for cooperative automation of large-scale connected vehicles. The task of cooperative automation is formulated as a centralized optimization problem taking the whole decision space of all vehicles into account. Considering the uncertainty of the environment, the problem is solved in a receding horizon fashion. Then, we employ the alternating direction method of multipliers (ADMM) to solve the centralized optimization in a parallel way, which scales more favorably to large-scale instances. Also, Taylor series is used to linearize nonconvex constraints caused by coupling collision avoidance constraints among interactive vehicles. Simulations with two typical traffic scenes for multiple vehicles demonstrate the effectiveness and efficiency of our method.

Zhiqian Lan, Yuxuan Jiang, Yao Mu et al.

Motion prediction is crucial for autonomous vehicles to operate safely in complex traffic environments. Extracting effective spatiotemporal relationships among traffic elements is key to accurate forecasting. Inspired by the successful practice of pretrained large language models, this paper presents SEPT, a modeling framework that leverages self-supervised learning to develop powerful spatiotemporal understanding for complex traffic scenes. Specifically, our approach involves three masking-reconstruction modeling tasks on scene inputs including agents' trajectories and road network, pretraining the scene encoder to capture kinematics within trajectory, spatial structure of road network, and interactions among roads and agents. The pretrained encoder is then finetuned on the downstream forecasting task. Extensive experiments demonstrate that SEPT, without elaborate architectural design or manual feature engineering, achieves state-of-the-art performance on the Argoverse 1 and Argoverse 2 motion forecasting benchmarks, outperforming previous methods on all main metrics by a large margin.

Jingliang Duan, Wenxuan Wang, Liming Xiao et al.

Reinforcement learning (RL) has shown remarkable success in solving complex decision-making and control tasks. However, many model-free RL algorithms experience performance degradation due to inaccurate value estimation, particularly the overestimation of Q-values, which can lead to suboptimal policies. To address this issue, we previously proposed the Distributional Soft Actor-Critic (DSAC or DSACv1), an off-policy RL algorithm that enhances value estimation accuracy by learning a continuous Gaussian value distribution. Despite its effectiveness, DSACv1 faces challenges such as training instability and sensitivity to reward scaling, caused by high variance in critic gradients due to return randomness. In this paper, we introduce three key refinements to DSACv1 to overcome these limitations and further improve Q-value estimation accuracy: expected value substitution, twin value distribution learning, and variance-based critic gradient adjustment. The enhanced algorithm, termed DSAC with Three refinements (DSAC-T or DSACv2), is systematically evaluated across a diverse set of benchmark tasks. Without the need for task-specific hyperparameter tuning, DSAC-T consistently matches or outperforms leading model-free RL algorithms, including SAC, TD3, DDPG, TRPO, and PPO, in all tested environments. Additionally, DSAC-T ensures a stable learning process and maintains robust performance across varying reward scales. Its effectiveness is further demonstrated through real-world application in controlling a wheeled robot, highlighting its potential for deployment in practical robotic tasks.

Zeyu Gao, Yao Mu, Chen Chen et al.

End-to-end autonomous driving provides a feasible way to automatically maximize overall driving system performance by directly mapping the raw pixels from a front-facing camera to control signals. Recent advanced methods construct a latent world model to map the high dimensional observations into compact latent space. However, the latent states embedded by the world model proposed in previous works may contain a large amount of task-irrelevant information, resulting in low sampling efficiency and poor robustness to input perturbations. Meanwhile, the training data distribution is usually unbalanced, and the learned policy is challenging to cope with the corner cases during the driving process. To solve the above challenges, we present a SEMantic Masked recurrent world model (SEM2), which introduces a semantic filter to extract key driving-relevant features and make decisions via the filtered features, and is trained with a multi-source data sampler, which aggregates common data and multiple corner case data in a single batch, to balance the data distribution. Extensive experiments on CARLA show our method outperforms the state-of-the-art approaches in terms of sample efficiency and robustness to input permutations.

Dongjie Yu, Haitong Ma, Shengbo Eben Li et al.

Constrained reinforcement learning (CRL) has gained significant interest recently, since safety constraints satisfaction is critical for real-world problems. However, existing CRL methods constraining discounted cumulative costs generally lack rigorous definition and guarantee of safety. In contrast, in the safe control research, safety is defined as persistently satisfying certain state constraints. Such persistent safety is possible only on a subset of the state space, called feasible set, where an optimal largest feasible set exists for a given environment. Recent studies incorporate feasible sets into CRL with energy-based methods such as control barrier function (CBF), safety index (SI), and leverage prior conservative estimations of feasible sets, which harms the performance of the learned policy. To deal with this problem, this paper proposes the reachability CRL (RCRL) method by using reachability analysis to establish the novel self-consistency condition and characterize the feasible sets. The feasible sets are represented by the safety value function, which is used as the constraint in CRL. We use the multi-time scale stochastic approximation theory to prove that the proposed algorithm converges to a local optimum, where the largest feasible set can be guaranteed. Empirical results on different benchmarks validate the learned feasible set, the policy performance, and constraint satisfaction of RCRL, compared to CRL and safe control baselines.

Yang Guan, Liye Tang, Chuanxiao Li et al.

Self-evolution is indispensable to realize full autonomous driving. This paper presents a self-evolving decision-making system based on the Integrated Decision and Control (IDC), an advanced framework built on reinforcement learning (RL). First, an RL algorithm called constrained mixed policy gradient (CMPG) is proposed to consistently upgrade the driving policy of the IDC. It adapts the MPG under the penalty method so that it can solve constrained optimization problems using both the data and model. Second, an attention-based encoding (ABE) method is designed to tackle the state representation issue. It introduces an embedding network for feature extraction and a weighting network for feature fusion, fulfilling order-insensitive encoding and importance distinguishing of road users. Finally, by fusing CMPG and ABE, we develop the first data-driven decision and control system under the IDC architecture, and deploy the system on a fully-functional self-driving vehicle running in daily operation. Experiment results show that boosting by data, the system can achieve better driving ability over model-based methods. It also demonstrates safe, efficient and smart driving behavior in various complex scenes at a signalized intersection with real mixed traffic flow.

Dongjie Yu, Wenjun Zou, Yujie Yang et al.

Safe reinforcement learning (RL) that solves constraint-satisfactory policies provides a promising way to the broader safety-critical applications of RL in real-world problems such as robotics. Among all safe RL approaches, model-based methods reduce training time violations further due to their high sample efficiency. However, lacking safety robustness against the model uncertainties remains an issue in safe model-based RL, especially in training time safety. In this paper, we propose a distributional reachability certificate (DRC) and its Bellman equation to address model uncertainties and characterize robust persistently safe states. Furthermore, we build a safe RL framework to resolve constraints required by the DRC and its corresponding shield policy. We also devise a line search method to maintain safety and reach higher returns simultaneously while leveraging the shield policy. Comprehensive experiments on classical benchmarks such as constrained tracking and navigation indicate that the proposed algorithm achieves comparable returns with much fewer constraint violations during training.

Siyi Lu, Lei He, Shengbo Eben Li et al.

End-to-end autonomous driving offers a streamlined alternative to the traditional modular pipeline, integrating perception, prediction, and planning within a single framework. While Deep Reinforcement Learning (DRL) has recently gained traction in this domain, existing approaches often overlook the critical connection between feature extraction of DRL and perception. In this paper, we bridge this gap by mapping the DRL feature extraction network directly to the perception phase, enabling clearer interpretation through semantic segmentation. By leveraging Bird's-Eye-View (BEV) representations, we propose a novel DRL-based end-to-end driving framework that utilizes multi-sensor inputs to construct a unified three-dimensional understanding of the environment. This BEV-based system extracts and translates critical environmental features into high-level abstract states for DRL, facilitating more informed control. Extensive experimental evaluations demonstrate that our approach not only enhances interpretability but also significantly outperforms state-of-the-art methods in autonomous driving control tasks, reducing the collision rate by 20%.

Jian Sun, Yuqi Dai, Chi-Man Vong et al.

Bird's-eye-view (BEV) semantic segmentation is becoming crucial in autonomous driving systems. It realizes ego-vehicle surrounding environment perception by projecting 2D multi-view images into 3D world space. Recently, BEV segmentation has made notable progress, attributed to better view transformation modules, larger image encoders, or more temporal information. However, there are still two issues: 1) a lack of effective understanding and enhancement of BEV space features, particularly in accurately capturing long-distance environmental features and 2) recognizing fine details of target objects. To address these issues, we propose OE-BevSeg, an end-to-end multimodal framework that enhances BEV segmentation performance through global environment-aware perception and local target object enhancement. OE-BevSeg employs an environment-aware BEV compressor. Based on prior knowledge about the main composition of the BEV surrounding environment varying with the increase of distance intervals, long-sequence global modeling is utilized to improve the model's understanding and perception of the environment. From the perspective of enriching target object information in segmentation results, we introduce the center-informed object enhancement module, using centerness information to supervise and guide the segmentation head, thereby enhancing segmentation performance from a local enhancement perspective. Additionally, we designed a multimodal fusion branch that integrates multi-view RGB image features with radar/LiDAR features, achieving significant performance improvements. Extensive experiments show that, whether in camera-only or multimodal fusion BEV segmentation tasks, our approach achieves state-of-the-art results by a large margin on the nuScenes dataset for vehicle segmentation, demonstrating superior applicability in the field of autonomous driving.

Jingliang Duan, Jie Li, Xuyang Chen et al.

In recent times, significant advancements have been made in delving into the optimization landscape of policy gradient methods for achieving optimal control in linear time-invariant (LTI) systems. Compared with state-feedback control, output-feedback control is more prevalent since the underlying state of the system may not be fully observed in many practical settings. This paper analyzes the optimization landscape inherent to policy gradient methods when applied to static output feedback (SOF) control in discrete-time LTI systems subject to quadratic cost. We begin by establishing crucial properties of the SOF cost, encompassing coercivity, L-smoothness, and M-Lipschitz continuous Hessian. Despite the absence of convexity, we leverage these properties to derive novel findings regarding convergence (and nearly dimension-free rate) to stationary points for three policy gradient methods, including the vanilla policy gradient method, the natural policy gradient method, and the Gauss-Newton method. Moreover, we provide proof that the vanilla policy gradient method exhibits linear convergence towards local minima when initialized near such minima. The paper concludes by presenting numerical examples that validate our theoretical findings. These results not only characterize the performance of gradient descent for optimizing the SOF problem but also provide insights into the effectiveness of general policy gradient methods within the realm of reinforcement learning.

Qingfan Wang, Dongyang Xu, Gaoyuan Kuang et al.

Trajectory prediction is significant for intelligent vehicles to achieve high-level autonomous driving, and a lot of relevant research achievements have been made recently. Despite the rapid development, most existing studies solely focused on normal safe scenarios while largely neglecting safety-critical scenarios, particularly those involving imminent collisions. This oversight may result in autonomous vehicles lacking the essential predictive ability in such situations, posing a significant threat to safety. To tackle these, this paper proposes a risk-aware trajectory prediction framework tailored to safety-critical scenarios. Leveraging distinctive hazardous features, we develop three core risk-aware components. First, we introduce a risk-incorporated scene encoder, which augments conventional encoders with quantitative risk information to achieve risk-aware encoding of hazardous scene contexts. Next, we incorporate endpoint-risk-combined intention queries as prediction priors in the decoder to ensure that the predicted multimodal trajectories cover both various spatial intentions and risk levels. Lastly, an auxiliary risk prediction task is implemented for the ultimate risk-aware prediction. Furthermore, to support model training and performance evaluation, we introduce a safety-critical trajectory prediction dataset and tailored evaluation metrics. We conduct comprehensive evaluations and compare our model with several SOTA models. Results demonstrate the superior performance of our model, with a significant improvement in most metrics. This prediction advancement enables autonomous vehicles to execute correct collision avoidance maneuvers under safety-critical scenarios, eventually enhancing road traffic safety.

Guojian Zhan, Likun Wang, Xiangteng Zhang et al.

Online planning has proven effective in reinforcement learning (RL) for improving sample efficiency and final performance. However, using planning for environment interaction inevitably introduces a divergence between the collected data and the policy's actual behaviors, degrading both model learning and policy improvement. To address this, we propose BOOM (Bootstrap Off-policy with WOrld Model), a framework that tightly integrates planning and off-policy learning through a bootstrap loop: the policy initializes the planner, and the planner refines actions to bootstrap the policy through behavior alignment. This loop is supported by a jointly learned world model, which enables the planner to simulate future trajectories and provides value targets to facilitate policy improvement. The core of BOOM is a likelihood-free alignment loss that bootstraps the policy using the planner's non-parametric action distribution, combined with a soft value-weighted mechanism that prioritizes high-return behaviors and mitigates variability in the planner's action quality within the replay buffer. Experiments on the high-dimensional DeepMind Control Suite and Humanoid-Bench show that BOOM achieves state-of-the-art results in both training stability and final performance. The code is accessible at https://github.com/molumitu/BOOM_MBRL.

Yuqi Dai, Jian Sun, Shengbo Eben Li et al.

Perception is essential for autonomous driving system. Recent approaches based on Bird's-eye-view (BEV) and deep learning have made significant progress. However, there exists challenging issues including lengthy development cycles, poor reusability, and complex sensor setups in perception algorithm development process. To tackle the above challenges, this paper proposes a novel hierarchical BEV perception paradigm, aiming to provide a library of fundamental perception modules and user-friendly graphical interface, enabling swift construction of customized models. We conduct the Pretrain-Finetune strategy to effectively utilize large scale public datasets and streamline development processes. Moreover, we present a Multi-Module Learning (MML) approach, enhancing performance through synergistic and iterative training of multiple models. Extensive experimental results on the Nuscenes dataset demonstrate that our approach renders significant improvement over the traditional training scheme.

Lei He, Qiaoyi Wang, Honglin Sun et al.

Visual bird's eye view (BEV) perception, due to its excellent perceptual capabilities, is progressively replacing costly LiDAR-based perception systems, especially in the realm of urban intelligent driving. However, this type of perception still relies on LiDAR data to construct ground truth databases, a process that is both cumbersome and time-consuming. Moreover, most massproduced autonomous driving systems are only equipped with surround camera sensors and lack LiDAR data for precise annotation. To tackle this challenge, we propose a fine-tuning method for BEV perception network based on visual 2D semantic perception, aimed at enhancing the model's generalization capabilities in new scene data. Considering the maturity and development of 2D perception technologies, our method significantly reduces the dependency on high-cost BEV ground truths and shows promising industrial application prospects. Extensive experiments and comparative analyses conducted on the nuScenes and Waymo public datasets demonstrate the effectiveness of our proposed method.

Yujie Yang, Zhilong Zheng, Shengbo Eben Li et al.

Safety is the priority concern when applying reinforcement learning (RL) algorithms to real-world control problems. While policy iteration provides a fundamental algorithm for standard RL, an analogous theoretical algorithm for safe RL remains absent. In this paper, we propose feasible policy iteration (FPI), the first foundational dynamic programming algorithm for safe RL. FPI alternates between policy evaluation, region identification and policy improvement. This follows actor-critic-scenery (ACS) framework where scenery refers to a feasibility function that represents a feasible region. A region-wise update rule is developed for the policy improvement step, which maximizes state-value function inside the feasible region and minimizes feasibility function outside it. With this update rule, FPI guarantees monotonic expansion of feasible region, monotonic improvement of state-value function, and geometric convergence to the optimal safe policy. Experimental results demonstrate that FPI achieves strictly zero constraint violation on low-dimensional tasks and outperforms existing methods in constraint adherence and reward performance on high-dimensional tasks.

Yuheng Lei, Jianyu Chen, Shengbo Eben Li et al.

Choosing an appropriate parameter set for the designed controller is critical for the final performance but usually requires a tedious and careful tuning process, which implies a strong need for automatic tuning methods. However, among existing methods, derivative-free ones suffer from poor scalability or low efficiency, while gradient-based ones are often unavailable due to possibly non-differentiable controller structure. To resolve the issues, we tackle the controller tuning problem using a novel derivative-free reinforcement learning (RL) framework, which performs timestep-wise perturbation in parameter space during experience collection and integrates derivative-free policy updates into the advanced actor-critic RL architecture to achieve high versatility and efficiency. To demonstrate the framework's efficacy, we conduct numerical experiments on two concrete examples from autonomous driving, namely, adaptive cruise control with PID controller and trajectory tracking with MPC controller. Experimental results show that the proposed method outperforms popular baselines and highlight its strong potential for controller tuning.

Jingliang Duan, Jie Li, Yinsong Ma et al.

Understanding the optimization landscape of linear quadratic regulation (LQR) problems is fundamental to the design of efficient reinforcement learning solutions. Recent work has made significant progress in characterizing the landscape of static output-feedback control and linear quadratic Gaussian (LQG) control. For LQG, much of the analysis leverages the separation principle, which allows the controller and estimator to be designed independently. However, this simplification breaks down when the gradients with respect to the estimator and controller parameters are inherently coupled, leading to a more intricate analysis. This paper investigates the optimization landscape of observer-based dynamic output-feedback control of LQR problems. We derive the optimal observer-controller pair in settings where transient quadratic performance cannot be neglected. Our analysis reveals that, in general, the combination of the standard LQR controller and the observer that minimizes the trace of the accumulated estimation error covariance does not correspond to a stationary point of the overall closed-loop performance objective. Moreover, we derive a pair of discrete-time Sylvester equations with symmetric structure, both involving the same set of matrix elements, that characterize the stationary point of the observer-based dynamic LQR problem. These equations offer analytical insight into the structure of the optimality conditions and provide a foundation for developing numerical policy gradient methods aimed at learning complex controllers that rely on reconstructed state information.

Xujie Song, Tong Liu, Shengbo Eben Li et al.

As a dedicated quantum device, Ising machines could solve large-scale binary optimization problems in milliseconds. There is emerging interest in utilizing Ising machines to train feedforward neural networks due to the prosperity of generative artificial intelligence. However, existing methods can only train single-layer feedforward networks because of the complex nonlinear network topology. This paper proposes an Ising learning algorithm to train quantized neural network (QNN), by incorporating two essential techinques, namely binary representation of topological network and order reduction of loss function. As far as we know, this is the first algorithm to train multi-layer feedforward networks on Ising machines, providing an alternative to gradient-based backpropagation. Firstly, training QNN is formulated as a quadratic constrained binary optimization (QCBO) problem by representing neuron connection and activation function as equality constraints. All quantized variables are encoded by binary bits based on binary encoding protocol. Secondly, QCBO is converted to a quadratic unconstrained binary optimization (QUBO) problem, that can be efficiently solved on Ising machines. The conversion leverages both penalty function and Rosenberg order reduction, who together eliminate equality constraints and reduce high-order loss function into a quadratic one. With some assumptions, theoretical analysis shows the space complexity of our algorithm is $\mathcal{O}(H^2L + HLN\log H)$, quantifying the required number of Ising spins. Finally, the algorithm effectiveness is validated with a simulated Ising machine on MNIST dataset. After annealing 700 ms, the classification accuracy achieves 98.3%. Among 100 runs, the success probability of finding the optimal solution is 72%. Along with the increasing number of spins on Ising machine, our algorithm has the potential to train deeper neural networks.

Haicheng Liao, Zhenning Li, Huanming Shen et al.

The ability to accurately predict the trajectory of surrounding vehicles is a critical hurdle to overcome on the journey to fully autonomous vehicles. To address this challenge, we pioneer a novel behavior-aware trajectory prediction model (BAT) that incorporates insights and findings from traffic psychology, human behavior, and decision-making. Our model consists of behavior-aware, interaction-aware, priority-aware, and position-aware modules that perceive and understand the underlying interactions and account for uncertainty and variability in prediction, enabling higher-level learning and flexibility without rigid categorization of driving behavior. Importantly, this approach eliminates the need for manual labeling in the training process and addresses the challenges of non-continuous behavior labeling and the selection of appropriate time windows. We evaluate BAT's performance across the Next Generation Simulation (NGSIM), Highway Drone (HighD), Roundabout Drone (RounD), and Macao Connected Autonomous Driving (MoCAD) datasets, showcasing its superiority over prevailing state-of-the-art (SOTA) benchmarks in terms of prediction accuracy and efficiency. Remarkably, even when trained on reduced portions of the training data (25%), our model outperforms most of the baselines, demonstrating its robustness and efficiency in predicting vehicle trajectories, and the potential to reduce the amount of data required to train autonomous vehicles, especially in corner cases. In conclusion, the behavior-aware model represents a significant advancement in the development of autonomous vehicles capable of predicting trajectories with the same level of proficiency as human drivers. The project page is available at https://github.com/Petrichor625/BATraj-Behavior-aware-Model.

Yangang Ren, Yao Lyu, Wenxuan Wang et al.

Zero-sum Markov Games (MGs) has been an efficient framework for multi-agent systems and robust control, wherein a minimax problem is constructed to solve the equilibrium policies. At present, this formulation is well studied under tabular settings wherein the maximum operator is primarily and exactly solved to calculate the worst-case value function. However, it is non-trivial to extend such methods to handle complex tasks, as finding the maximum over large-scale action spaces is usually cumbersome. In this paper, we propose the smoothing policy iteration (SPI) algorithm to solve the zero-sum MGs approximately, where the maximum operator is replaced by the weighted LogSumExp (WLSE) function to obtain the nearly optimal equilibrium policies. Specially, the adversarial policy is served as the weight function to enable an efficient sampling over action spaces.We also prove the convergence of SPI and analyze its approximation error in $\infty -$norm based on the contraction mapping theorem. Besides, we propose a model-based algorithm called Smooth adversarial Actor-critic (SaAC) by extending SPI with the function approximations. The target value related to WLSE function is evaluated by the sampled trajectories and then mean square error is constructed to optimize the value function, and the gradient-ascent-descent methods are adopted to optimize the protagonist and adversarial policies jointly. In addition, we incorporate the reparameterization technique in model-based gradient back-propagation to prevent the gradient vanishing due to sampling from the stochastic policies. We verify our algorithm in both tabular and function approximation settings. Results show that SPI can approximate the worst-case value function with a high accuracy and SaAC can stabilize the training process and improve the adversarial robustness in a large margin.

Zeyang Li, Chuxiong Hu, Yunan Wang et al.

Reinforcement learning (RL) agents are vulnerable to adversarial disturbances, which can deteriorate task performance or compromise safety specifications. Existing methods either address safety requirements under the assumption of no adversary (e.g., safe RL) or only focus on robustness against performance adversaries (e.g., robust RL). Learning one policy that is both safe and robust remains a challenging open problem. The difficulty is how to tackle two intertwined aspects in the worst cases: feasibility and optimality. Optimality is only valid inside a feasible region, while identification of maximal feasible region must rely on learning the optimal policy. To address this issue, we propose a systematic framework to unify safe RL and robust RL, including problem formulation, iteration scheme, convergence analysis and practical algorithm design. This unification is built upon constrained two-player zero-sum Markov games. A dual policy iteration scheme is proposed, which simultaneously optimizes a task policy and a safety policy. The convergence of this iteration scheme is proved. Furthermore, we design a deep RL algorithm for practical implementation, called dually robust actor-critic (DRAC). The evaluations with safety-critical benchmarks demonstrate that DRAC achieves high performance and persistent safety under all scenarios (no adversary, safety adversary, performance adversary), outperforming all baselines significantly.

Yuxuan Jiang, Yujie Yang, Zhiqian Lan et al.

Rocket recycling is a crucial pursuit in aerospace technology, aimed at reducing costs and environmental impact in space exploration. The primary focus centers on rocket landing control, involving the guidance of a nonlinear underactuated rocket with limited fuel in real-time. This challenging task prompts the application of reinforcement learning (RL), yet goal-oriented nature of the problem poses difficulties for standard RL algorithms due to the absence of intermediate reward signals. This paper, for the first time, significantly elevates the success rate of rocket landing control from 8% with a baseline controller to 97% on a high-fidelity rocket model using RL. Our approach, called Random Annealing Jump Start (RAJS), is tailored for real-world goal-oriented problems by leveraging prior feedback controllers as guide policy to facilitate environmental exploration and policy learning in RL. In each episode, the guide policy navigates the environment for the guide horizon, followed by the exploration policy taking charge to complete remaining steps. This jump-start strategy prunes exploration space, rendering the problem more tractable to RL algorithms. The guide horizon is sampled from a uniform distribution, with its upper bound annealing to zero based on performance metrics, mitigating distribution shift and mismatch issues in existing methods. Additional enhancements, including cascading jump start, refined reward and terminal condition, and action smoothness regulation, further improve policy performance and practical applicability. The proposed method is validated through extensive evaluation and Hardware-in-the-Loop testing, affirming the effectiveness, real-time feasibility, and smoothness of the proposed controller.

Bowyn Tan, Yutong Xie, Bai Huang et al.

High-fidelity street scene reconstruction is pivotal for end-to-end autonomous driving simulation, where novel-view synthesis (NVS) and time-varying information modeling are two fundamental capabilities to facilitate closed-loop training. However, existing 3DGS methods and their 4D extensions fail to simultaneously achieve both. To bridge this gap, we establish an information-geometric diagnostic framework, revealing that this limitation stems from a credit assignment dilemma between spatial and temporal parameters. Specifically, the deterministic coupling between viewpoint and time in single-source observation creates a low-rank structure that induces massive null-space ambiguity between static view-dependent and dynamic time-varying components. Temporal information overshadows spatial cues, causing the estimation variance of spatial parameters to diverge. To address this issue, we propose Orthogonal Projected Gradient (OPG), a hierarchical training method designed to restore spatial identifiability. OPG prioritizes the integrity of spatial representations by securing them in an initial stage, then restricts temporal updates to the spatial null space, enabling proactive credit assignment. While OPG isolates temporal updates algebraically, Temporal Regularization Strategy is proposed to further refine the temporal solution space by imposing a smoothness constraint based on the physical prior of consistent appearance evolution, ensuring that the reconstructed scene remains physically consistent in closed-loop simulation. Extensive experiments demonstrate that our method not only maintains stable NVS capabilities but also demonstrates superior performance in traditional observation-reproducing metrics, which indirectly reflect the capability of modeling temporal dynamics.

Zeyang Li, Chuxiong Hu, Shengbo Eben Li et al.

Safety is a primary concern when applying reinforcement learning to real-world control tasks, especially in the presence of external disturbances. However, existing safe reinforcement learning algorithms rarely account for external disturbances, limiting their applicability and robustness in practice. To address this challenge, this paper proposes a robust safe reinforcement learning framework that tackles worst-case disturbances. First, this paper presents a policy iteration scheme to solve for the robust invariant set, i.e., a subset of the safe set, where persistent safety is only possible for states within. The key idea is to establish a two-player zero-sum game by leveraging the safety value function in Hamilton-Jacobi reachability analysis, in which the protagonist (i.e., control inputs) aims to maintain safety and the adversary (i.e., external disturbances) tries to break down safety. This paper proves that the proposed policy iteration algorithm converges monotonically to the maximal robust invariant set. Second, this paper integrates the proposed policy iteration scheme into a constrained reinforcement learning algorithm that simultaneously synthesizes the robust invariant set and uses it for constrained policy optimization. This algorithm tackles both optimality and safety, i.e., learning a policy that attains high rewards while maintaining safety under worst-case disturbances. Experiments on classic control tasks show that the proposed method achieves zero constraint violation with learned worst-case adversarial disturbances, while other baseline algorithms violate the safety constraints substantially. Our proposed method also attains comparable performance as the baselines even in the absence of the adversary.

Wenhan Cao, Tianyi Zhang, Zeju Sun et al.

Practical Bayes filters often assume the state distribution of each time step to be Gaussian for computational tractability, resulting in the so-called Gaussian filters. When facing nonlinear systems, Gaussian filters such as extended Kalman filter (EKF) or unscented Kalman filter (UKF) typically rely on certain linearization techniques, which can introduce large estimation errors. To address this issue, this paper reconstructs the prediction and update steps of Gaussian filtering as solutions to two distinct optimization problems, whose optimal conditions are found to have analytical forms from Stein's lemma. It is observed that the stationary point for the prediction step requires calculating the first two moments of the prior distribution, which is equivalent to that step in existing moment-matching filters. In the update step, instead of linearizing the model to approximate the stationary points, we propose an iterative approach to directly minimize the update step's objective to avoid linearization errors. For the purpose of performing the steepest descent on the Gaussian manifold, we derive its natural gradient that leverages Fisher information matrix to adjust the gradient direction, accounting for the curvature of the parameter space. Combining this update step with moment matching in the prediction step, we introduce a new iterative filter for nonlinear systems called \textit{N}atural Gr\textit{a}dient Gaussia\textit{n} Appr\textit{o}ximation filter, or NANO filter for short. We prove that NANO filter locally converges to the optimal Gaussian approximation at each time step. Furthermore, the estimation error is proven exponentially bounded for nearly linear measurement equation and low noise levels through constructing a supermartingale-like property across consecutive time steps.

Wei Wu, Honglin Chen, Wenhan Cao et al.

Tightly coupled SLAM formulations under mixed-rate sensing often bind temporal processing, local geometric association, estimator formulation, and map-update policy into method-specific designs. Such binding makes it difficult to vary one design choice without re-engineering the rest of the state-estimation process. This paper presents FUSE, a framework for unified state estimation in robotic SLAM systems. FUSE organizes the state-estimation interface around observation ingestion, propagation, update, and state query, and uses this interface to separate temporal processing, residual-ready local geometric association, estimator formulation, and map-update policy. A LiDAR--IMU instantiation is developed to examine the framework under mixed-rate sensing and directional degeneracy, where high-rate inertial propagation, LiDAR-triggered geometric update, residual screening, and degeneracy-aware correction operate through the same interface boundaries. On a 418 m loop-corridor sequence, the instantiation reports a 1.626~m end-to-end trajectory error, corresponding to a 7.9% relative error reduction compared with Faster-LIO, the lowest-error baseline on this sequence. The results support FUSE as a framework for organizing state-estimation design choices and show how the evaluated instantiation regularizes updates along weakly observable directions.

Enhui Ma, Jiahuan Zhang, Guantian Zheng et al.

Multimodal Large Language Models (MLLMs) are rapidly becoming the intelligence brain of end-to-end autonomous driving systems. A key challenge is to assess whether MLLMs can truly understand and follow complex real-world traffic rules. However, existing benchmarks mainly focus on single-rule scenarios like traffic sign recognition, neglecting the complexity of multi-rule concurrency and conflicts in real driving. Consequently, models perform well on simple tasks but often fail or violate rules in real world complex situations. To bridge this gap, we propose DriveCombo, a text and vision-based benchmark for compositional traffic rule reasoning. Inspired by human drivers' cognitive development, we propose a systematic Five-Level Cognitive Ladder that evaluates reasoning from single-rule understanding to multi-rule integration and conflict resolution, enabling quantitative assessment across cognitive stages. We further propose a Rule2Scene Agent that maps language-based traffic rules to dynamic driving scenes through rule crafting and scene generation, enabling scene-level traffic rule visual reasoning. Evaluations of 14 mainstream MLLMs reveal performance drops as task complexity grows, particularly during rule conflicts. After splitting the dataset and fine-tuning on the training set, we further observe substantial improvements in both traffic rule reasoning and downstream planning capabilities. These results highlight the effectiveness of DriveCombo in advancing compliant and intelligent autonomous driving systems.

Tianyi Zhang, Wenhan Cao, Shengbo Eben Li

Popular Bayes filters often apply linearization techniques, such as Taylor expansion or stochastic linear regression, to enable the use of the Kalman filter structure, but this can lead to large errors in strongly nonlinear systems. The recently proposed NANO filter addresses this issue by interpreting the prediction and update steps of Bayesian filtering as two distinct optimization problems and solving them through moment matching and natural gradient descent, thereby avoiding model linearization errors. However, the natural gradient update in NANO can occasionally diverge because the posterior covariance in its iteration may lose positive definiteness. Our analysis shows that the posterior covariance is the sum of the inverse prior covariance and the expected Hessian of the log-likelihood function, and that the indefiniteness of the latter term is the root cause of update failure. To address this issue, we propose two remedies. The first approximates the log-likelihood Hessian using the Gauss-Newton method, representing it as the self-adjoint product of the Jacobian of the normalized measurement residual, which is guaranteed to be positive semi-definite. The second reformulates the covariance update as an exponential-form update of the Cholesky factor and reconstructs the covariance via its Gram matrix, which ensures positive definiteness. Experiments on three classical nonlinear systems demonstrate that the proposed NANO filter with guaranteed positive definiteness outperforms popular members of the Kalman filter family and original NANO filter.

Tianyi Zhang, Wenhan Cao, Chang Liu et al.

Accurate state estimation for robotic systems evolving on Lie group manifolds, such as legged robots, is a prerequisite for achieving agile control. However, this task is challenged by nonlinear observation models defined on curved manifolds, where existing filters rely on local linearization in the tangent space to handle such nonlinearity, leading to accumulated estimation errors. To address this limitation, we reformulate manifold filtering as a parameter optimization problem over a Gaussian-distributed increment variable, thereby avoiding linearization. Under this formulation, the increment can be mapped to the Lie group through the exponential operator, where it acts multiplicatively on the prior estimate to yield the posterior state. We further propose a natural gradient optimization scheme for solving this problem, whose iteration process leverages the Fisher information matrix of the increment variable to account for the curvature of the tangent space. This results in an iterative algorithm named the Natural Gradient Gaussian Approximation on Lie Groups (NANO-L) filter. Leveraging the perturbation model in Lie derivative, we prove that for the invariant observation model widely adopted in robotic localization tasks, the covariance update in NANO-L admits an exact closed-form solution, eliminating the need for iterative updates thus improving computational efficiency. Hardware experiments on a Unitree GO2 legged robot operating across different terrains demonstrate that NANO-L achieves approximately 40% lower estimation error than commonly used filters at a comparable computational cost.

Tianze Zhu, Yinuo Wang, Wenjun Zou et al.

Reinforcement learning (RL) is a fundamental methodology in autonomous driving systems, where generative policies exhibit considerable potential by leveraging their ability to model complex distributions to enhance exploration. However, their inherent high inference latency severely impedes their deployment in real-time decision-making and control. To address this issue, we propose diffusion actor-critic with entropy regulator via flow matching (DACER-F) by introducing flow matching into online RL, enabling the generation of competitive actions in a single inference step. By leveraging Langevin dynamics and gradients of the Q-function, DACER-F dynamically optimizes actions from experience replay toward a target distribution that balances high Q-value information with exploratory behavior. The flow policy is then trained to efficiently learn a mapping from a simple prior distribution to this dynamic target. In complex multi-lane and intersection simulations, DACER-F outperforms baselines diffusion actor-critic with entropy regulator (DACER) and distributional soft actor-critic (DSAC), while maintaining an ultra-low inference latency. DACER-F further demonstrates its scalability on standard RL benchmark DeepMind Control Suite (DMC), achieving a score of 775.8 in the humanoid-stand task and surpassing prior methods. Collectively, these results establish DACER-F as a high-performance and computationally efficient RL algorithm.

Zeyang Li, Chuxiong Hu, Yunan Wang et al.

Regularization is one of the most important techniques in reinforcement learning algorithms. The well-known soft actor-critic algorithm is a special case of regularized policy iteration where the regularizer is chosen as Shannon entropy. Despite some empirical success of regularized policy iteration, its theoretical underpinnings remain unclear. This paper proves that regularized policy iteration is strictly equivalent to the standard Newton-Raphson method in the condition of smoothing out Bellman equation with strongly convex functions. This equivalence lays the foundation of a unified analysis for both global and local convergence behaviors of regularized policy iteration. We prove that regularized policy iteration has global linear convergence with the rate being $γ$ (discount factor). Furthermore, this algorithm converges quadratically once it enters a local region around the optimal value. We also show that a modified version of regularized policy iteration, i.e., with finite-step policy evaluation, is equivalent to inexact Newton method where the Newton iteration formula is solved with truncated iterations. We prove that the associated algorithm achieves an asymptotic linear convergence rate of $γ^M$ in which $M$ denotes the number of steps carried out in policy evaluation. Our results take a solid step towards a better understanding of the convergence properties of regularized policy iteration algorithms.

Zhanwen Liu, Yujing Sun, Yang Wang et al.

The dynamic range limitation of conventional RGB cameras reduces global contrast and causes loss of high-frequency details such as textures and edges in complex traffic environments (e.g., nighttime driving, tunnels), hindering discriminative feature extraction and degrading frame-based object detection. To address this, we integrate a bio-inspired event camera with an RGB camera to provide high dynamic range information and propose a motion cue fusion network (MCFNet), which achieves optimal spatiotemporal alignment and adaptive cross-modal feature fusion under challenging lighting. Specifically, an event correction module (ECM) temporally aligns asynchronous event streams with image frames via optical-flow-based warping, jointly optimized with the detection network to learn task-aware event representations. The event dynamic upsampling module (EDUM) enhances spatial resolution of event frames to match image structures, ensuring precise spatiotemporal alignment. The cross-modal mamba fusion module (CMM) uses adaptive feature fusion with a novel interlaced scanning mechanism, effectively integrating complementary information for robust detection. Experiments conducted on the DSEC-Det and PKU-DAVIS-SOD datasets demonstrate that MCFNet significantly outperforms existing methods in various poor lighting and fast moving traffic scenarios. Notably, on the DSEC-Det dataset, MCFNet achieves a remarkable improvement, surpassing the best existing methods by 7.4% in mAP50 and 1.7% in mAP metrics, respectively. The code is available at https://github.com/Charm11492/MCFNet.

Yujie Yang, Zhilong Zheng, Masayoshi Tomizuka et al.

Satisfying safety constraints is a priority concern when solving optimal control problems (OCPs). Due to the existence of infeasibility phenomenon, where a constraint-satisfying solution cannot be found, it is necessary to identify a feasible region before implementing a policy. Existing feasibility theories built for model predictive control (MPC) only consider the feasibility of optimal policy. However, reinforcement learning (RL), as another important control method, solves the optimal policy in an iterative manner, which comes with a series of non-optimal intermediate policies. Feasibility analysis of these non-optimal policies is also necessary for iteratively improving constraint satisfaction; but that is not available under existing MPC feasibility theories. This paper proposes a feasibility theory that applies to both MPC and RL by filling in the missing part of feasibility analysis for an arbitrary policy. The basis of our theory is to decouple policy solving and implementation into two temporal domains: virtual-time domain and real-time domain. This allows us to separately define initial and endless, state and policy feasibility, and their corresponding feasible regions. Based on these definitions, we analyze the containment relationships between different feasible regions, which enables us to describe the feasible region of an arbitrary policy. We further provide virtual-time constraint design rules along with a practical design tool called feasibility function that helps to achieve the maximum feasible region. We review most of existing constraint formulations and point out that they are essentially applications of feasibility functions in different forms. We demonstrate our feasibility theory by visualizing different feasible regions under both MPC and RL policies in an emergency braking control task.

Jiaming Zhang, Yujie Yang, Haoning Wang et al.

Safe reinforcement learning (safe RL) aims to respect safety requirements while optimizing long-term performance. In many practical applications, however, the problem involves an infinite number of constraints, known as semi-infinite safe RL (SI-safe RL). Such constraints typically appear when safety conditions must be enforced across an entire continuous parameter space, such as ensuring adequate resource distribution at every spatial location. In this paper, we propose exchange policy optimization (EPO), an algorithmic framework that achieves optimal policy performance and deterministic bounded safety. EPO works by iteratively solving safe RL subproblems with finite constraint sets and adaptively adjusting the active set through constraint expansion and deletion. At each iteration, constraints with violations exceeding the predefined tolerance are added to refine the policy, while those with zero Lagrange multipliers are removed after the policy update. This exchange rule prevents uncontrolled growth of the working set and supports effective policy training. Our theoretical analysis demonstrates that, under mild assumptions, strategies trained via EPO achieve performance comparable to optimal solutions with global constraint violations strictly remaining within a prescribed bound.

Shiqi Liu, Zeyu He, Guojian Zhan et al.

Reinforcement Learning (RL) has significantly improved large language model reasoning, but existing RL fine-tuning methods rely heavily on heuristic techniques such as entropy regularization and reweighting to maintain stability. In practice, they often suffer from late-stage performance collapse, leading to degraded reasoning quality and unstable training. Our analysis shows that the magnitude of token-wise policy gradients in RL is negatively correlated with token probability and local policy entropy. We find that training instability can be caused by a tiny fraction of tokens, approximately 0.01\%, which we term \emph{spurious tokens}. When such tokens appear in correct responses, they contribute little to the reasoning outcome but inherit the full sequence-level reward, leading to abnormally amplified gradient updates. To mitigate this instability, we design S2T (silencing spurious tokens) mechanism to efficiently identify spurious tokens through characteristic signals with low probability, low entropy, and positive advantage, and then to suppress their gradient perturbations during optimization. Incorporating this mechanism into a group-based objective, we propose Spurious-Token-Aware Policy Optimization (STAPO), which promotes stable and effective large-scale model refinement. Across six mathematical reasoning benchmarks using Qwen 1.7B, 8B, and 14B base models, STAPO consistently demonstrates superior entropy stability and achieves an average performance improvement of 7.13\% ($ρ_{\mathrm{T}}$=1.0, top-p=1.0) and 3.69\% ($ρ_{\mathrm{T}}$=0.7, top-p=0.9) over GRPO, 20-Entropy and JustRL.

Haicheng Liao, Yongkang Li, Zhenning Li et al.

In autonomous vehicle (AV) technology, the ability to accurately predict the movements of surrounding vehicles is paramount for ensuring safety and operational efficiency. Incorporating human decision-making insights enables AVs to more effectively anticipate the potential actions of other vehicles, significantly improving prediction accuracy and responsiveness in dynamic environments. This paper introduces the Human-Like Trajectory Prediction (HLTP) model, which adopts a teacher-student knowledge distillation framework inspired by human cognitive processes. The HLTP model incorporates a sophisticated teacher-student knowledge distillation framework. The "teacher" model, equipped with an adaptive visual sector, mimics the visual processing of the human brain, particularly the functions of the occipital and temporal lobes. The "student" model focuses on real-time interaction and decision-making, drawing parallels to prefrontal and parietal cortex functions. This approach allows for dynamic adaptation to changing driving scenarios, capturing essential perceptual cues for accurate prediction. Evaluated using the Macao Connected and Autonomous Driving (MoCAD) dataset, along with the NGSIM and HighD benchmarks, HLTP demonstrates superior performance compared to existing models, particularly in challenging environments with incomplete data. The project page is available at Github.

Yinan Zheng, Ruiming Liang, Kexin Zheng et al. · tsinghua

Achieving human-like driving behaviors in complex open-world environments is a critical challenge in autonomous driving. Contemporary learning-based planning approaches such as imitation learning methods often struggle to balance competing objectives and lack of safety assurance,due to limited adaptability and inadequacy in learning complex multi-modal behaviors commonly exhibited in human planning, not to mention their strong reliance on the fallback strategy with predefined rules. We propose a novel transformer-based Diffusion Planner for closed-loop planning, which can effectively model multi-modal driving behavior and ensure trajectory quality without any rule-based refinement. Our model supports joint modeling of both prediction and planning tasks under the same architecture, enabling cooperative behaviors between vehicles. Moreover, by learning the gradient of the trajectory score function and employing a flexible classifier guidance mechanism, Diffusion Planner effectively achieves safe and adaptable planning behaviors. Evaluations on the large-scale real-world autonomous planning benchmark nuPlan and our newly collected 200-hour delivery-vehicle driving dataset demonstrate that Diffusion Planner achieves state-of-the-art closed-loop performance with robust transferability in diverse driving styles.

Chang Liu, Wenhan Cao, Zeju Sun et al.

Bayesian filtering is a cornerstone of state estimation in complex systems such as aerospace systems, yet exact solutions are available only for linear Gaussian models. In practice,nonlinear systems are handled through tractable approximations,with Gaussian filters such as the extended and unscented Kalman filters being among the most widely used methods. This tutorial revisits Gaussian filtering from an information-geometric perspective, viewing the prediction and measurement update steps as inference procedures over state distributions. Within this framework, we introduce a geometry-aware Gaussian filtering approach that leverages natural gradient descent on the statistical manifold of Gaussian distributions. The resulting Natural Gradient Gaussian Approximation (NANO) filter iteratively refines the posterior mean and covariance while respecting the intrinsic geometry of the Gaussian family and preserving the positive definiteness of the covariance matrix. We further highlight fundamental connections to the classical Kalman filtering, showing that a single natural-gradient step exactly recovers the Kalman measurement update in the linear-Gaussian case. The practical implications of the proposed framework are illustrated through case studies in representative nonlinear estimation problems,including satellite attitude estimation, simultaneous localization and mapping, and state estimation for robotic systems including quadruped and humanoid robots.

Jiaming Zhang, Yujie Yang, Yao Lyu et al.

Safety is a primary challenge in real-world reinforcement learning (RL). Formulating safety requirements as state-wise constraints has become a prominent paradigm. Handling state-wise constraints with the Lagrangian method requires a distinct multiplier for every state, necessitating neural networks to approximate them as a multiplier network. However, applying standard dual gradient ascent to multiplier networks induces severe training oscillations. This is because the inherent instability of dual ascent is exacerbated by network generalization -- local overshoots and delayed updates propagate to adjacent states, further amplifying policy fluctuations. Existing stabilization techniques are designed for scalar multipliers, which are inadequate for state-dependent multiplier networks. To address this challenge, we propose an augmented Lagrangian multiplier network (ALaM) framework for stable learning of state-wise multipliers. ALaM consists of two key components. First, a quadratic penalty is introduced into the augmented Lagrangian to compensate for delayed multiplier updates and establish the local convexity near the optimum, thereby mitigating policy oscillations. Second, the multiplier network is trained via supervised regression toward a dual target, which stabilizes training and promotes convergence. Theoretically, we show that ALaM guarantees multiplier convergence and thus recovers the optimal policy of the constrained problem. Building on this framework, we integrate soft actor-critic (SAC) with ALaM to develop the SAC-ALaM algorithm. Experiments demonstrate that SAC-ALaM outperforms state-of-the-art safe RL baselines in both safety and return, while also stabilizing training dynamics and learning well-calibrated multipliers for risk identification.

Haicheng Liao, Chengyue Wang, Kaiqun Zhu et al.

In mixed autonomous driving environments, accurately predicting the future trajectories of surrounding vehicles is crucial for the safe operation of autonomous vehicles (AVs). In driving scenarios, a vehicle's trajectory is determined by the decision-making process of human drivers. However, existing models primarily focus on the inherent statistical patterns in the data, often neglecting the critical aspect of understanding the decision-making processes of human drivers. This oversight results in models that fail to capture the true intentions of human drivers, leading to suboptimal performance in long-term trajectory prediction. To address this limitation, we introduce a Cognitive-Informed Transformer (CITF) that incorporates a cognitive concept, Perceived Safety, to interpret drivers' decision-making mechanisms. Perceived Safety encapsulates the varying risk tolerances across drivers with different driving behaviors. Specifically, we develop a Perceived Safety-aware Module that includes a Quantitative Safety Assessment for measuring the subject risk levels within scenarios, and Driver Behavior Profiling for characterizing driver behaviors. Furthermore, we present a novel module, Leanformer, designed to capture social interactions among vehicles. CITF demonstrates significant performance improvements on three well-established datasets. In terms of long-term prediction, it surpasses existing benchmarks by 12.0% on the NGSIM, 28.2% on the HighD, and 20.8% on the MoCAD dataset. Additionally, its robustness in scenarios with limited or missing data is evident, surpassing most state-of-the-art (SOTA) baselines, and paving the way for real-world applications.

Tong Liu, Yinuo Wang, Xujie Song et al.

Reinforcement learning has been proven to be highly effective in handling complex control tasks. Traditional methods typically use unimodal distributions, such as Gaussian distributions, to model the output of value distributions. However, unimodal distribution often and easily causes bias in value function estimation, leading to poor algorithm performance. This paper proposes a distributional reinforcement learning algorithm called DSAC-D (Distributed Soft Actor Critic with Diffusion Policy) to address the challenges of estimating bias in value functions and obtaining multimodal policy representations. A multimodal distributional policy iteration framework that can converge to the optimal policy was established by introducing policy entropy and value distribution function. A diffusion value network that can accurately characterize the distribution of multi peaks was constructed by generating a set of reward samples through reverse sampling using a diffusion model. Based on this, a distributional reinforcement learning algorithm with dual diffusion of the value network and the policy network was derived. MuJoCo testing tasks demonstrate that the proposed algorithm not only learns multimodal policy, but also achieves state-of-the-art (SOTA) performance in all 9 control tasks, with significant suppression of estimation bias and total average return improvement of over 10% compared to existing mainstream algorithms. The results of real vehicle testing show that DSAC-D can accurately characterize the multimodal distribution of different driving styles, and the diffusion policy network can characterize multimodal trajectories.

Yinuo Wang, Likun Wang, Mining Tan et al.

Due to their expressive capacity, diffusion models have shown great promise in offline RL and imitation learning. Diffusion Actor-Critic with Entropy Regulator (DACER) extended this capability to online RL by using the reverse diffusion process as a policy approximator, achieving state-of-the-art performance. However, it still suffers from a core trade-off: more diffusion steps ensure high performance but reduce efficiency, while fewer steps degrade performance. This remains a major bottleneck for deploying diffusion policies in real-time online RL. To mitigate this, we propose DACERv2, which leverages a Q-gradient field objective with respect to action as an auxiliary optimization target to guide the denoising process at each diffusion step, thereby introducing intermediate supervisory signals that enhance the efficiency of single-step diffusion. Additionally, we observe that the independence of the Q-gradient field from the diffusion time step is inconsistent with the characteristics of the diffusion process. To address this issue, a temporal weighting mechanism is introduced, allowing the model to effectively eliminate large-scale noise during the early stages and refine its outputs in the later stages. Experimental results on OpenAI Gym benchmarks and multimodal tasks demonstrate that, compared with classical and diffusion-based online RL algorithms, DACERv2 achieves higher performance in most complex control environments with only five diffusion steps and shows greater multimodality.

Tianqi Zhang, Puzhen Yuan, Guojian Zhan et al.

Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal evolution of a feedback control system. Classical constrained optimization methods, such as penalty and Lagrangian approaches, inherently use proportional and integral feedback controllers. In this paper, we propose a more generic equivalence framework to build the connection between constrained optimization and feedback control system, for the purpose of developing more effective constrained RL algorithms. Firstly, we define that each step of the system evolution determines the Lagrange multiplier by solving a multiplier feedback optimal control problem (MFOCP). In this problem, the control input is multiplier, the state is policy parameters, the dynamics is described by policy gradient descent, and the objective is to minimize constraint violations. Then, we introduce a multiplier guided policy learning (MGPL) module to perform policy parameters updating. And we prove that the resulting optimal policy, achieved through alternating MFOCP and MGPL, aligns with the solution of the primal constrained RL problem, thereby establishing our equivalence framework. Furthermore, we point out that the existing PID Lagrangian is merely one special case within our framework that utilizes a PID controller. We also accommodate the integration of other various feedback controllers, thereby facilitating the development of new algorithms. As a representative, we employ model predictive control (MPC) as the feedback controller and consequently propose a new algorithm called predictive Lagrangian optimization (PLO). Numerical experiments demonstrate its superiority over the PID Lagrangian method, achieving a larger feasible region up to 7.2% and a comparable average reward.

Wenhan Cao, Shiqi Liu, Chang Liu et al.

Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is critical to state distribution inference. Previously, the conditional probability is assumed to be exactly known, which represents a measure of the occurrence probability of one event, given the second event. In this paper, we find that by adding an additional event that stipulates an inequality condition, we can transform the conditional probability into a special integration that is analogous to convolution. Based on this transformation, we show that both transition probability and output probability can be generalized to convolutional forms, resulting in a more general filtering framework that we call convolutional Bayesian filtering. This new framework encompasses standard Bayesian filtering as a special case when the distance metric of the inequality condition is selected as Dirac delta function. It also allows for a more nuanced consideration of model mismatch by choosing different types of inequality conditions. For instance, when the distance metric is defined in a distributional sense, the transition probability and output probability can be approximated by simply rescaling them into fractional powers. Under this framework, a robust version of Kalman filter can be constructed by only altering the noise covariance matrix, while maintaining the conjugate nature of Gaussian distributions. Finally, we exemplify the effectiveness of our approach by reshaping classic filtering algorithms into convolutional versions, including Kalman filter, extended Kalman filter, unscented Kalman filter and particle filter.

Guojian Zhan, Ziang Zheng, Shengbo Eben Li

The design of feedback controllers is undergoing a paradigm shift from modelic (i.e., model-driven) control to datatic (i.e., data-driven) control. Canonical form of state space model is an important concept in modelic control systems, exemplified by Jordan form, controllable form and observable form, whose purpose is to facilitate system analysis and controller synthesis. In the realm of datatic control, there is a notable absence in the standardization of data-based system representation. This paper for the first time introduces the concept of canonical data form for the purpose of achieving more effective design of datatic controllers. In a control system, the data sample in canonical form consists of a transition component and an attribute component. The former encapsulates the plant dynamics at the sampling time independently, which is a tuple containing three elements: a state, an action and their corresponding next state. The latter describes one or some artificial characteristics of the current sample, whose calculation must be performed in an online manner. The attribute of each sample must adhere to two requirements: (1) causality, ensuring independence from any future samples; and (2) locality, allowing dependence on historical samples but constrained to a finite neighboring set. The purpose of adding attribute is to offer some kinds of benefits for controller design in terms of effectiveness and efficiency. To provide a more close-up illustration, we present two canonical data forms: temporal form and spatial form, and demonstrate their advantages in reducing instability and enhancing training efficiency in two datatic control systems.

Yao Lyu, Xiangteng Zhang, Shengbo Eben Li et al.

Training deep reinforcement learning (RL) agents necessitates overcoming the highly unstable nonconvex stochastic optimization inherent in the trial-and-error mechanism. To tackle this challenge, we propose a physics-inspired optimization algorithm called relativistic adaptive gradient descent (RAD), which enhances long-term training stability. By conceptualizing neural network (NN) training as the evolution of a conformal Hamiltonian system, we present a universal framework for transferring long-term stability from conformal symplectic integrators to iterative NN updating rules, where the choice of kinetic energy governs the dynamical properties of resulting optimization algorithms. By utilizing relativistic kinetic energy, RAD incorporates principles from special relativity and limits parameter updates below a finite speed, effectively mitigating abnormal gradient influences. Additionally, RAD models NN optimization as the evolution of a multi-particle system where each trainable parameter acts as an independent particle with an individual adaptive learning rate. We prove RAD's sublinear convergence under general nonconvex settings, where smaller gradient variance and larger batch sizes contribute to tighter convergence. Notably, RAD degrades to the well-known adaptive moment estimation (ADAM) algorithm when its speed coefficient is chosen as one and symplectic factor as a small positive value. Experimental results show RAD outperforming nine baseline optimizers with five RL algorithms across twelve environments, including standard benchmarks and challenging scenarios. Notably, RAD achieves up to a 155.1% performance improvement over ADAM in Atari games, showcasing its efficacy in stabilizing and accelerating RL training.

Shiqi Liu, Wenhan Cao, Chang Liu et al.

Estimating hidden states in dynamical systems, also known as optimal filtering, is a long-standing problem in various fields of science and engineering. In this paper, we introduce a general filtering framework, \textbf{LLM-Filter}, which leverages large language models (LLMs) for state estimation by embedding noisy observations with text prototypes. In various experiments for classical dynamical systems, we find that first, state estimation can significantly benefit from the reasoning knowledge embedded in pre-trained LLMs. By achieving proper modality alignment with the frozen LLM, LLM-Filter outperforms the state-of-the-art learning-based approaches. Second, we carefully design the prompt structure, System-as-Prompt (SaP), incorporating task instructions that enable the LLM to understand the estimation tasks. Guided by these prompts, LLM-Filter exhibits exceptional generalization, capable of performing filtering tasks accurately in changed or even unseen environments. We further observe a scaling-law behavior in LLM-Filter, where accuracy improves with larger model sizes and longer training times. These findings make LLM-Filter a promising foundation model of filtering.

Ziang Zheng, Guojian Zhan, Bin Shuai et al.

Reinforcement learning (RL) has demonstrated remarkable capability in acquiring robot skills, but learning each new skill still requires substantial data collection for training. The pretrain-and-finetune paradigm offers a promising approach for efficiently adapting to new robot entities and tasks. Inspired by the idea that acquired knowledge can accelerate learning new tasks with the same robot and help a new robot master a trained task, we propose a latent training framework where a transferable latent-to-latent locomotion policy is pretrained alongside diverse task-specific observation encoders and action decoders. This policy in latent space processes encoded latent observations to generate latent actions to be decoded, with the potential to learn general abstract motion skills. To retain essential information for decision-making and control, we introduce a diffusion recovery module that minimizes information reconstruction loss during pretrain stage. During fine-tune stage, the pretrained latent-to-latent locomotion policy remains fixed, while only the lightweight task-specific encoder and decoder are optimized for efficient adaptation. Our method allows a robot to leverage its own prior experience across different tasks as well as the experience of other morphologically diverse robots to accelerate adaptation. We validate our approach through extensive simulations and real-world experiments, demonstrating that the pretrained latent-to-latent locomotion policy effectively generalizes to new robot entities and tasks with improved efficiency.