Jingliang Duan

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.

Xuyang Chen, Jingliang Duan, Yingbin Liang et al.

The actor-critic (AC) reinforcement learning algorithms have been the powerhouse behind many challenging applications. Nevertheless, its convergence is fragile in general. To study its instability, existing works mostly consider the uncommon double-loop variant or basic models with finite state and action space. We investigate the more practical single-sample two-timescale AC for solving the canonical linear quadratic regulator (LQR) problem, where the actor and the critic update only once with a single sample in each iteration on an unbounded continuous state and action space. Existing analysis cannot conclude the convergence for such a challenging case. We develop a new analysis framework that allows establishing the global convergence to an $ε$-optimal solution with at most an $\mathcal{O}(ε^{-2.5})$ sample complexity. To our knowledge, this is the first finite-time convergence analysis for the single sample two-timescale AC for solving LQR with global optimality. The sample complexity improves those of other variants by orders, which sheds light on the practical wisdom of single sample algorithms. We also further validate our theoretical findings via comprehensive simulation comparisons.

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.

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.

Jingliang Duan, Wenhan Cao, Yang Zheng et al.

The convergence of policy gradient algorithms in reinforcement learning hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of linear quadratic control. However, most of the existing literature only considers the optimization landscape for static full-state or output feedback policies (controllers). We investigate the more challenging case of dynamic output-feedback policies for linear quadratic regulation (abbreviated as dLQR), which is prevalent in practice but has a rather complicated optimization landscape. We first show how the dLQR cost varies with the coordinate transformation of the dynamic controller and then derive the optimal transformation for a given observable stabilizing controller. At the core of our results is the uniqueness of the stationary point of dLQR when it is observable, which is in a concise form of an observer-based controller with the optimal similarity transformation. These results shed light on designing efficient algorithms for general decision-making problems with partially observed information.

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.

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.

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.

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.

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.

Jiang Wu, Sichao Wu, Yinsong Ma et al.

Industrial accidents, particularly in high-risk domains such as surface and underground mining, are frequently caused by unsafe worker behaviors. Traditional manual inspection remains labor-intensive, error-prone, and insufficient for large-scale, dynamic environments, highlighting the urgent need for intelligent and automated safety monitoring. In this paper, we present MonitorVLM, a novel vision--language framework designed to detect safety violations directly from surveillance video streams. MonitorVLM introduces three key innovations: (1) a domain-specific violation dataset comprising 9,000 vision--question--answer (VQA) samples across 40 high-frequency mining regulations, enriched with augmentation and auxiliary detection cues; (2) a clause filter (CF) module that dynamically selects the Top-$K$ most relevant clauses, reducing inference latency by 13.56\% while maintaining accuracy; and (3) a behavior magnifier (BM) module that enhances worker regions to improve fine-grained action recognition, yielding additional gains of 3.45% in precision and 8.62% in recall. Experimental results demonstrate that MonitorVLM significantly outperforms baseline vision--language models, achieving improvements of 22.01% in precision, 34.22\% in recall, and 28.37% in F1 score over the 72B unfine-tuned baseline. A lightweight web-based interface further integrates MonitorVLM into practical workflows, enabling automatic violation reporting with video timestamping. This study highlights the potential of multimodal large models to enhance occupational safety monitoring in mining and beyond.

Xuyang Chen, Jingliang Duan, Lin Zhao

Actor-critic methods have achieved state-of-the-art performance in various challenging tasks. However, theoretical understandings of their performance remain elusive and challenging. Existing studies mostly focus on practically uncommon variants such as double-loop or two-timescale stepsize actor-critic algorithms for simplicity. These results certify local convergence on finite state- or action-space only. We push the boundary to investigate the classic single-sample single-timescale actor-critic on continuous (infinite) state-action space, where we employ the canonical linear quadratic regulator (LQR) problem as a case study. We show that the popular single-timescale actor-critic can attain an epsilon-optimal solution with an order of epsilon to -2 sample complexity for solving LQR on the demanding continuous state-action space. Our work provides new insights into the performance of single-timescale actor-critic, which further bridges the gap between theory and practice.

Likun Wang, Xiangteng Zhang, Yinuo Wang et al.

Exploration is fundamental to reinforcement learning (RL), as it determines how effectively an agent discovers and exploits the underlying structure of its environment to achieve optimal performance. Existing exploration methods generally fall into two categories: active exploration and passive exploration. The former introduces stochasticity into the policy but struggles in high-dimensional environments, while the latter adaptively prioritizes transitions in the replay buffer to enhance exploration, yet remains constrained by limited sample diversity. To address the limitation in passive exploration, we propose Modelic Generative Exploration (MoGE), which augments exploration through the generation of under-explored critical states and synthesis of dynamics-consistent experiences through transition models. MoGE is composed of two components: (1) a diffusion-based generator that synthesizes critical states under the guidance of a utility function evaluating each state's potential influence on policy exploration, and (2) a one-step imagination world model for constructing critical transitions based on the critical states for agent learning. Our method adopts a modular formulation that aligns with the principles of off-policy learning, allowing seamless integration with existing algorithms to improve exploration without altering their core structures. Empirical results on OpenAI Gym and DeepMind Control Suite reveal that MoGE effectively bridges exploration and policy learning, leading to remarkable gains in both sample efficiency and performance across complex control tasks.

Guojian Zhan, Likun Wang, Pengcheng Wang et al.

Maximum entropy has become a mainstream off-policy reinforcement learning (RL) framework for balancing exploitation and exploration. However, two bottlenecks still limit further performance improvement: (1) non-stationary Q-value estimation caused by jointly injecting entropy and updating its weighting parameter, i.e., temperature; and (2) short-sighted local entropy tuning that adjusts temperature only according to the current single-step entropy, without considering the effect of cumulative entropy over time. In this paper, we extends maximum entropy framework by proposing a trajectory entropy-constrained reinforcement learning (TECRL) framework to address these two challenges. Within this framework, we first separately learn two Q-functions, one associated with reward and the other with entropy, ensuring clean and stable value targets unaffected by temperature updates. Then, the dedicated entropy Q-function, explicitly quantifying the expected cumulative entropy, enables us to enforce a trajectory entropy constraint and consequently control the policy long-term stochasticity. Building on this TECRL framework, we develop a practical off-policy algorithm, DSAC-E, by extending the state-of-the-art distributional soft actor-critic with three refinements (DSAC-T). Empirical results on the OpenAI Gym benchmark demonstrate that our DSAC-E can achieve higher returns and better stability.

Feihong Zhang, Guojian Zhan, Bin Shuai et al.

Reinforcement learning (RL), known for its self-evolution capability, offers a promising approach to training high-level autonomous driving systems. However, handling constraints remains a significant challenge for existing RL algorithms, particularly in real-world applications. In this paper, we propose a new safety-oriented training technique called harmonic policy iteration (HPI). At each RL iteration, it first calculates two policy gradients associated with efficient driving and safety constraints, respectively. Then, a harmonic gradient is derived for policy updating, minimizing conflicts between the two gradients and consequently enabling a more balanced and stable training process. Furthermore, we adopt the state-of-the-art DSAC algorithm as the backbone and integrate it with our HPI to develop a new safe RL algorithm, DSAC-H. Extensive simulations in multi-lane scenarios demonstrate that DSAC-H achieves efficient driving performance with near-zero safety constraint violations.

Wenjun Zou, Yao Lyu, Jie Li et al.

Safe reinforcement learning (RL) offers advanced solutions to constrained optimal control problems. Existing studies in safe RL implicitly assume continuity in policy functions, where policies map states to actions in a smooth, uninterrupted manner; however, our research finds that in some scenarios, the feasible policy should be discontinuous or multi-valued, interpolating between discontinuous local optima can inevitably lead to constraint violations. We are the first to identify the generating mechanism of such a phenomenon, and employ topological analysis to rigorously prove the existence of policy bifurcation in safe RL, which corresponds to the contractibility of the reachable tuple. Our theorem reveals that in scenarios where the obstacle-free state space is non-simply connected, a feasible policy is required to be bifurcated, meaning its output action needs to change abruptly in response to the varying state. To train such a bifurcated policy, we propose a safe RL algorithm called multimodal policy optimization (MUPO), which utilizes a Gaussian mixture distribution as the policy output. The bifurcated behavior can be achieved by selecting the Gaussian component with the highest mixing coefficient. Besides, MUPO also integrates spectral normalization and forward KL divergence to enhance the policy's capability of exploring different modes. Experiments with vehicle control tasks show that our algorithm successfully learns the bifurcated policy and ensures satisfying safety, while a continuous policy suffers from inevitable constraint violations.

Haoqi Yan, Haoyuan Xu, Hongbo Gao et al.

Intelligent drill boom hole-seeking is a promising technology for enhancing drilling efficiency, mitigating potential safety hazards, and relieving human operators. Most existing intelligent drill boom control methods rely on a hierarchical control framework based on inverse kinematics. However, these methods are generally time-consuming due to the computational complexity of inverse kinematics and the inefficiency of the sequential execution of multiple joints. To tackle these challenges, this study proposes an integrated drill boom control method based on Reinforcement Learning (RL). We develop an integrated drill boom control framework that utilizes a parameterized policy to directly generate control inputs for all joints at each time step, taking advantage of joint posture and target hole information. By formulating the hole-seeking task as a Markov decision process, contemporary mainstream RL algorithms can be directly employed to learn a hole-seeking policy, thus eliminating the need for inverse kinematics solutions and promoting cooperative multi-joint control. To enhance the drilling accuracy throughout the entire drilling process, we devise a state representation that combines Denavit-Hartenberg joint information and preview hole-seeking discrepancy data. Simulation results show that the proposed method significantly outperforms traditional methods in terms of hole-seeking accuracy and time efficiency.

Yangang Ren, Jianhua Jiang, Dongjie Yu et al.

Intersection is one of the most complex and accident-prone urban scenarios for autonomous driving wherein making safe and computationally efficient decisions is non-trivial. Current research mainly focuses on the simplified traffic conditions while ignoring the existence of mixed traffic flows, i.e., vehicles, cyclists and pedestrians. For urban roads, different participants leads to a quite dynamic and complex interaction, posing great difficulty to learn an intelligent policy. This paper develops the dynamic permutation state representation in the framework of integrated decision and control (IDC) to handle signalized intersections with mixed traffic flows. Specially, this representation introduces an encoding function and summation operator to construct driving states from environmental observation, capable of dealing with different types and variant number of traffic participants. A constrained optimal control problem is built wherein the objective involves tracking performance and the constraints for different participants and signal lights are designed respectively to assure safety. We solve this problem by offline optimizing encoding function, value function and policy function, wherein the reasonable state representation will be given by the encoding function and then served as the input of policy and value function. An off-policy training is designed to reuse observations from driving environment and backpropagation through time is utilized to update the policy function and encoding function jointly. Verification result shows that the dynamic permutation state representation can enhance the driving performance of IDC, including comfort, decision compliance and safety with a large margin. The trained driving policy can realize efficient and smooth passing in the complex intersection, guaranteeing driving intelligence and safety simultaneously.

Jingliang Duan, Yangang Ren, Fawang Zhang et al.

In this paper, we propose a new reinforcement learning (RL) algorithm, called encoding distributional soft actor-critic (E-DSAC), for decision-making in autonomous driving. Unlike existing RL-based decision-making methods, E-DSAC is suitable for situations where the number of surrounding vehicles is variable and eliminates the requirement for manually pre-designed sorting rules, resulting in higher policy performance and generality. We first develop an encoding distributional policy iteration (DPI) framework by embedding a permutation invariant module, which employs a feature neural network (NN) to encode the indicators of each vehicle, in the distributional RL framework. The proposed DPI framework is proved to exhibit important properties in terms of convergence and global optimality. Next, based on the developed encoding DPI framework, we propose the E-DSAC algorithm by adding the gradient-based update rule of the feature NN to the policy evaluation process of the DSAC algorithm. Then, the multi-lane driving task and the corresponding reward function are designed to verify the effectiveness of the proposed algorithm. Results show that the policy learned by E-DSAC can realize efficient, smooth, and relatively safe autonomous driving in the designed scenario. And the final policy performance learned by E-DSAC is about three times that of DSAC. Furthermore, its effectiveness has also been verified in real vehicle experiments.

Baiyu Peng, Jingliang Duan, Jianyu Chen et al.

Safety is essential for reinforcement learning (RL) applied in the real world. Adding chance constraints (or probabilistic constraints) is a suitable way to enhance RL safety under uncertainty. Existing chance-constrained RL methods like the penalty methods and the Lagrangian methods either exhibit periodic oscillations or learn an over-conservative or unsafe policy. In this paper, we address these shortcomings by proposing a separated proportional-integral Lagrangian (SPIL) algorithm. We first review the constrained policy optimization process from a feedback control perspective, which regards the penalty weight as the control input and the safe probability as the control output. Based on this, the penalty method is formulated as a proportional controller, and the Lagrangian method is formulated as an integral controller. We then unify them and present a proportional-integral Lagrangian method to get both their merits, with an integral separation technique to limit the integral value in a reasonable range. To accelerate training, the gradient of safe probability is computed in a model-based manner. We demonstrate our method can reduce the oscillations and conservatism of RL policy in a car-following simulation. To prove its practicality, we also apply our method to a real-world mobile robot navigation task, where our robot successfully avoids a moving obstacle with highly uncertain or even aggressive behaviors.

Jingliang Duan, Dongjie Yu, Shengbo Eben Li et al.

In this paper, we propose a new state representation method, called encoding sum and concatenation (ESC), for the state representation of decision-making in autonomous driving. Unlike existing state representation methods, ESC is applicable to a variable number of surrounding vehicles and eliminates the need for manually pre-designed sorting rules, leading to higher representation ability and generality. The proposed ESC method introduces a representation neural network (NN) to encode each surrounding vehicle into an encoding vector, and then adds these vectors to obtain the representation vector of the set of surrounding vehicles. By concatenating the set representation with other variables, such as indicators of the ego vehicle and road, we realize the fixed-dimensional and permutation invariant state representation. This paper has further proved that the proposed ESC method can realize the injective representation if the output dimension of the representation NN is greater than the number of variables of all surrounding vehicles. This means that by taking the ESC representation as policy inputs, we can find the nearly optimal representation NN and policy NN by simultaneously optimizing them using gradient-based updating. Experiments demonstrate that compared with the fixed-permutation representation method, the proposed method improves the representation ability of the surrounding vehicles, and the corresponding approximation error is reduced by 62.2%.

Yang Guan, Yangang Ren, Qi Sun et al.

Decision and control are core functionalities of high-level automated vehicles. Current mainstream methods, such as functionality decomposition and end-to-end reinforcement learning (RL), either suffer high time complexity or poor interpretability and adaptability on real-world autonomous driving tasks. In this paper, we present an interpretable and computationally efficient framework called integrated decision and control (IDC) for automated vehicles, which decomposes the driving task into static path planning and dynamic optimal tracking that are structured hierarchically. First, the static path planning generates several candidate paths only considering static traffic elements. Then, the dynamic optimal tracking is designed to track the optimal path while considering the dynamic obstacles. To that end, we formulate a constrained optimal control problem (OCP) for each candidate path, optimize them separately and follow the one with the best tracking performance. To unload the heavy online computation, we propose a model-based reinforcement learning (RL) algorithm that can be served as an approximate constrained OCP solver. Specifically, the OCPs for all paths are considered together to construct a single complete RL problem and then solved offline in the form of value and policy networks, for real-time online path selecting and tracking respectively. We verify our framework in both simulations and the real world. Results show that compared with baseline methods IDC has an order of magnitude higher online computing efficiency, as well as better driving performance including traffic efficiency and safety. In addition, it yields great interpretability and adaptability among different driving tasks. The effectiveness of the proposed method is also demonstrated in real road tests with complicated traffic conditions.

Kaiming Tang, Shengbo Eben Li, Yuming Yin et al.

State estimation is critical to control systems, especially when the states cannot be directly measured. This paper presents an approximate optimal filter, which enables to use policy iteration technique to obtain the steady-state gain in linear Gaussian time-invariant systems. This design transforms the optimal filtering problem with minimum mean square error into an optimal control problem, called Approximate Optimal Filtering (AOF) problem. The equivalence holds given certain conditions about initial state distributions and policy formats, in which the system state is the estimation error, control input is the filter gain, and control objective function is the accumulated estimation error. We present a policy iteration algorithm to solve the AOF problem in steady-state. A classic vehicle state estimation problem finally evaluates the approximate filter. The results show that the policy converges to the steady-state Kalman gain, and its accuracy is within 2 %.

Yiting Kong, Yang Guan, Jingliang Duan et al.

Merging into the highway from the on-ramp is an essential scenario for automated driving. The decision-making under the scenario needs to balance the safety and efficiency performance to optimize a long-term objective, which is challenging due to the dynamic, stochastic, and adversarial characteristics. The Rule-based methods often lead to conservative driving on this task while the learning-based methods have difficulties meeting the safety requirements. In this paper, we propose an RL-based end-to-end decision-making method under a framework of offline training and online correction, called the Shielded Distributional Soft Actor-critic (SDSAC). The SDSAC adopts the policy evaluation with safety consideration and a safety shield parameterized with the barrier function in its offline training and online correction, respectively. These two measures support each other for better safety while not damaging the efficiency performance severely. We verify the SDSAC on an on-ramp merge scenario in simulation. The results show that the SDSAC has the best safety performance compared to baseline algorithms and achieves efficient driving simultaneously.

Zhengyu Liu, Jingliang Duan, Wenxuan Wang et al.

This paper proposes an off-line algorithm, called Recurrent Model Predictive Control (RMPC), to solve general nonlinear finite-horizon optimal control problems. Unlike traditional Model Predictive Control (MPC) algorithms, it can make full use of the current computing resources and adaptively select the longest model prediction horizon. Our algorithm employs a recurrent function to approximate the optimal policy, which maps the system states and reference values directly to the control inputs. The number of prediction steps is equal to the number of recurrent cycles of the learned policy function. With an arbitrary initial policy function, the proposed RMPC algorithm can converge to the optimal policy by directly minimizing the designed loss function. We further prove the convergence and optimality of the RMPC algorithm thorough Bellman optimality principle, and demonstrate its generality and efficiency using two numerical examples.

Yang Guan, Jingliang Duan, Shengbo Eben Li et al.

Reinforcement learning (RL) shows great potential in sequential decision-making. At present, mainstream RL algorithms are data-driven, which usually yield better asymptotic performance but much slower convergence compared with model-driven methods. This paper proposes mixed policy gradient (MPG) algorithm, which fuses the empirical data and the transition model in policy gradient (PG) to accelerate convergence without performance degradation. Formally, MPG is constructed as a weighted average of the data-driven and model-driven PGs, where the former is the derivative of the learned Q-value function, and the latter is that of the model-predictive return. To guide the weight design, we analyze and compare the upper bound of each PG error. Relying on that, a rule-based method is employed to heuristically adjust the weights. In particular, to get a better PG, the weight of the data-driven PG is designed to grow along the learning process while the other to decrease. Simulation results show that the MPG method achieves the best asymptotic performance and convergence speed compared with other baseline algorithms.

Baiyu Peng, Yao Mu, Jingliang Duan et al.

Safety is essential for reinforcement learning (RL) applied in real-world tasks like autonomous driving. Chance constraints which guarantee the satisfaction of state constraints at a high probability are suitable to represent the requirements in real-world environment with uncertainty. Existing chance constrained RL methods like the penalty method and the Lagrangian method either exhibit periodic oscillations or cannot satisfy the constraints. In this paper, we address these shortcomings by proposing a separated proportional-integral Lagrangian (SPIL) algorithm. Taking a control perspective, we first interpret the penalty method and the Lagrangian method as proportional feedback and integral feedback control, respectively. Then, a proportional-integral Lagrangian method is proposed to steady learning process while improving safety. To prevent integral overshooting and reduce conservatism, we introduce the integral separation technique inspired by PID control. Finally, an analytical gradient of the chance constraint is utilized for model-based policy optimization. The effectiveness of SPIL is demonstrated by a narrow car-following task. Experiments indicate that compared with previous methods, SPIL improves the performance while guaranteeing safety, with a steady learning process.

Jie Li, Shengbo Eben Li, Yang Guan et al.

The uncertainties in plant dynamics remain a challenge for nonlinear control problems. This paper develops a ternary policy iteration (TPI) algorithm for solving nonlinear robust control problems with bounded uncertainties. The controller and uncertainty of the system are considered as game players, and the robust control problem is formulated as a two-player zero-sum differential game. In order to solve the differential game, the corresponding Hamilton-Jacobi-Isaacs (HJI) equation is then derived. Three loss functions and three update phases are designed to match the identity equation, minimization and maximization of the HJI equation, respectively. These loss functions are defined by the expectation of the approximate Hamiltonian in a generated state set to prevent operating all the states in the entire state set concurrently. The parameters of value function and policies are directly updated by diminishing the designed loss functions using the gradient descent method. Moreover, zero-initialization can be applied to the parameters of the control policy. The effectiveness of the proposed TPI algorithm is demonstrated through two simulation studies. The simulation results show that the TPI algorithm can converge to the optimal solution for the linear plant, and has high resistance to disturbances for the nonlinear plant.

Lu Wen, Jingliang Duan, Shengbo Eben Li et al.

Reinforcement learning (RL) is attracting increasing interests in autonomous driving due to its potential to solve complex classification and control problems. However, existing RL algorithms are rarely applied to real vehicles for two predominant problems: behaviours are unexplainable, and they cannot guarantee safety under new scenarios. This paper presents a safe RL algorithm, called Parallel Constrained Policy Optimization (PCPO), for two autonomous driving tasks. PCPO extends today's common actor-critic architecture to a three-component learning framework, in which three neural networks are used to approximate the policy function, value function and a newly added risk function, respectively. Meanwhile, a trust region constraint is added to allow large update steps without breaking the monotonic improvement condition. To ensure the feasibility of safety constrained problems, synchronized parallel learners are employed to explore different state spaces, which accelerates learning and policy-update. The simulations of two scenarios for autonomous vehicles confirm we can ensure safety while achieving fast learning.

Yangang Ren, Jingliang Duan, Shengbo Eben Li et al.

Reinforcement learning (RL) has achieved remarkable performance in numerous sequential decision making and control tasks. However, a common problem is that learned nearly optimal policy always overfits to the training environment and may not be extended to situations never encountered during training. For practical applications, the randomness of environment usually leads to some devastating events, which should be the focus of safety-critical systems such as autonomous driving. In this paper, we introduce the minimax formulation and distributional framework to improve the generalization ability of RL algorithms and develop the Minimax Distributional Soft Actor-Critic (Minimax DSAC) algorithm. Minimax formulation aims to seek optimal policy considering the most severe variations from environment, in which the protagonist policy maximizes action-value function while the adversary policy tries to minimize it. Distributional framework aims to learn a state-action return distribution, from which we can model the risk of different returns explicitly, thereby formulating a risk-averse protagonist policy and a risk-seeking adversarial policy. We implement our method on the decision-making tasks of autonomous vehicles at intersections and test the trained policy in distinct environments. Results demonstrate that our method can greatly improve the generalization ability of the protagonist agent to different environmental variations.

Jingliang Duan, Yang Guan, Shengbo Eben Li et al.

In reinforcement learning (RL), function approximation errors are known to easily lead to the Q-value overestimations, thus greatly reducing policy performance. This paper presents a distributional soft actor-critic (DSAC) algorithm, which is an off-policy RL method for continuous control setting, to improve the policy performance by mitigating Q-value overestimations. We first discover in theory that learning a distribution function of state-action returns can effectively mitigate Q-value overestimations because it is capable of adaptively adjusting the update stepsize of the Q-value function. Then, a distributional soft policy iteration (DSPI) framework is developed by embedding the return distribution function into maximum entropy RL. Finally, we present a deep off-policy actor-critic variant of DSPI, called DSAC, which directly learns a continuous return distribution by keeping the variance of the state-action returns within a reasonable range to address exploding and vanishing gradient problems. We evaluate DSAC on the suite of MuJoCo continuous control tasks, achieving the state-of-the-art performance.

Yang Guan, Shengbo Eben Li, Jingliang Duan et al.

Reinforcement learning (RL) algorithms have been successfully applied to a range of challenging sequential decision making and control tasks. In this paper, we classify RL into direct and indirect RL according to how they seek the optimal policy of the Markov decision process problem. The former solves the optimal policy by directly maximizing an objective function using gradient descent methods, in which the objective function is usually the expectation of accumulative future rewards. The latter indirectly finds the optimal policy by solving the Bellman equation, which is the sufficient and necessary condition from Bellman's principle of optimality. We study policy gradient forms of direct and indirect RL and show that both of them can derive the actor-critic architecture and can be unified into a policy gradient with the approximate value function and the stationary state distribution, revealing the equivalence of direct and indirect RL. We employ a Gridworld task to verify the influence of different forms of policy gradient, suggesting their differences and relationships experimentally. Finally, we classify current mainstream RL algorithms using the direct and indirect taxonomy, together with other ones including value-based and policy-based, model-based and model-free.

Jingliang Duan, Zhengyu Liu, Shengbo Eben Li et al.

This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Firstly, a constrained generalized policy iteration (CGPI) framework is developed to handle state constraints by transforming the traditional policy improvement process into a constrained policy optimization problem. Next, we propose an actor-critic variant of CGPI, called CADP, in which both policy and value functions are approximated by multi-layer neural networks to directly map the system states to control inputs and value function, respectively. CADP linearizes the constrained optimization problem locally into a quadratically constrained linear programming problem, and then obtains the optimal update of the policy network by solving its dual problem. A trust region constraint is added to prevent excessive policy update, thus ensuring linearization accuracy. We determine the feasibility of the policy optimization problem by calculating the minimum trust region boundary and update the policy using two recovery rules when infeasible. The vehicle control problem in the path-tracking task is used to demonstrate the effectiveness of this proposed method.

Jingliang Duan, Jie Li, Qiang Ge et al.

This paper presents the Relaxed Continuous-Time Actor-critic (RCTAC) algorithm, a method for finding the nearly optimal policy for nonlinear continuous-time (CT) systems with known dynamics and infinite horizon, such as the path-tracking control of vehicles. RCTAC has several advantages over existing adaptive dynamic programming algorithms for CT systems. It does not require the ``admissibility" of the initialized policy or the input-affine nature of controlled systems for convergence. Instead, given any initial policy, RCTAC can converge to an admissible, and subsequently nearly optimal policy for a general nonlinear system with a saturated controller. RCTAC consists of two phases: a warm-up phase and a generalized policy iteration phase. The warm-up phase minimizes the square of the Hamiltonian to achieve admissibility, while the generalized policy iteration phase relaxes the update termination conditions for faster convergence. The convergence and optimality of the algorithm are proven through Lyapunov analysis, and its effectiveness is demonstrated through simulations and real-world path-tracking tasks.