arXiv subjects

Jingliang Duan

Publications and source records attributed to Jingliang Duan.

At least 37 records · Page 2Linked to original sources

arXiv2024

Guiding Reinforcement Learning with Incomplete System Dynamics

Model-free reinforcement learning (RL) is inherently a reactive method, operating under the assumption that it starts with no prior knowledge of the system and entirely depends on trial-and-error for learning. This approach faces several challenges, such as poor sample efficiency, generalization, and the need for well-designed reward functions to guide learning effectively. On the other hand, controllers based on complete system dynamics do not require data. This paper addresses the intermediate situation where there is not enough model information for complete controller design, but there is enough to suggest that a model-free approach is not the best approach either. By carefully decoupling known and unknown information about the system dynamics, we obtain an embedded controller guided by our partial model and thus improve the learning efficiency of an RL-enhanced approach. A modular design allows us to deploy mainstream RL algorithms to refine the policy. Simulation results show that our method significantly improves sample efficiency compared with standard RL methods on continuous control tasks, and also offers enhanced performance over traditional control approaches. Experiments on a real ground vehicle also validate the performance of our method, including generalization and robustness.

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arXiv2024

Enhance Sample Efficiency and Robustness of End-to-end Urban Autonomous Driving via Semantic Masked World Model

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.

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arXiv2024

Policy Bifurcation in Safe Reinforcement Learning

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.

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arXiv2024

Mixed Policy Gradient: off-policy reinforcement learning driven jointly by data and model

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.

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arXiv2023

Integrated Drill Boom Hole-Seeking Control via Reinforcement Learning

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.

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arXiv2023

Training Multi-layer Neural Networks on Ising Machine

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.

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arXiv2023

On the Optimization Landscape of Dynamic Output Feedback: A Case Study for Linear Quadratic Regulator

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.

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arXiv2023

On the Optimization Landscape of Dynamic Output Feedback Linear Quadratic Control

The convergence of policy gradient algorithms 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. One of our core results is the uniqueness of the stationary point of dLQR when it is observable, which provides an optimality certificate for solving dynamic controllers using policy gradient methods. Moreover, we establish conditions under which dLQR and linear quadratic Gaussian control are equivalent, thus providing a unified viewpoint of optimal control of both deterministic and stochastic linear systems. These results further shed light on designing policy gradient algorithms for more general decision-making problems with partially observed information.

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arXiv2023

Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedback

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.

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arXiv2023

Relaxed Actor-Critic with Convergence Guarantees for Continuous-Time Optimal Control of Nonlinear Systems

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.

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arXiv2023

Global Convergence of Two-timescale Actor-Critic for Solving Linear Quadratic Regulator

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.

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arXiv2022

Smoothing Policy Iteration for Zero-sum Markov Games

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.

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arXiv2022

Safe Model-Based Reinforcement Learning with an Uncertainty-Aware Reachability Certificate

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.

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arXiv2022

Improve Generalization of Driving Policy at Signalized Intersections with Adversarial Learning

Intersections are quite challenging among various driving scenes wherein the interaction of signal lights and distinct traffic actors poses great difficulty to learn a wise and robust driving policy. Current research rarely considers the diversity of intersections and stochastic behaviors of traffic participants. For practical applications, the randomness usually leads to some devastating events, which should be the focus of autonomous driving. This paper introduces an adversarial learning paradigm to boost the intelligence and robustness of driving policy for signalized intersections with dense traffic flow. Firstly, we design a static path planner which is capable of generating trackable candidate paths for multiple intersections with diversified topology. Next, a constrained optimal control problem (COCP) is built based on these candidate paths wherein the bounded uncertainty of dynamic models is considered to capture the randomness of driving environment. We propose adversarial policy gradient (APG) to solve the COCP wherein the adversarial policy is introduced to provide disturbances by seeking the most severe uncertainty while the driving policy learns to handle this situation by competition. Finally, a comprehensive system is established to conduct training and testing wherein the perception module is introduced and the human experience is incorporated to solve the yellow light dilemma. Experiments indicate that the trained policy can handle the signal lights flexibly meanwhile realizing the smooth and efficient passing with a humanoid paradigm. Besides, APG enables a large-margin improvement of the resistance to the abnormal behaviors and thus ensures a high safety level for the autonomous vehicle.

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arXiv2022

Adaptive dynamic programming for nonaffine nonlinear optimal control problem with state constraints

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.

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arXiv2022

Recurrent Model Predictive Control: Learning an Explicit Recurrent Controller for Nonlinear Systems

This paper proposes an offline control algorithm, called Recurrent Model Predictive Control (RMPC), to solve large-scale nonlinear finite-horizon optimal control problems. It can be regarded as an explicit solver of traditional Model Predictive Control (MPC) algorithms, which can adaptively select appropriate model prediction horizon according to current computing resources, so as to improve the policy performance. 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 output of the learned policy network after N recurrent cycles corresponds to the nearly optimal solution of N-step MPC. A policy optimization objective is designed by decomposing the MPC cost function according to the Bellman's principle of optimality. The optimal recurrent policy can be obtained by directly minimizing the designed objective function, which is applicable for general nonlinear and non input-affine systems. Both simulation-based and real-robot path-tracking tasks are utilized to demonstrate the effectiveness of the proposed method.

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arXiv2022

Primal-dual Estimator Learning: an Offline Constrained Moving Horizon Estimation Method with Feasibility and Near-optimality Guarantees

This paper proposes a primal-dual framework to learn a stable estimator for linear constrained estimation problems leveraging the moving horizon approach. To avoid the online computational burden in most existing methods, we learn a parameterized function offline to approximate the primal estimate. Meanwhile, a dual estimator is trained to check the suboptimality of the primal estimator during execution time. Both the primal and dual estimators are learned from data using supervised learning techniques, and the explicit sample size is provided, which enables us to guarantee the quality of each learned estimator in terms of feasibility and optimality. This in turn allows us to bound the probability of the learned estimator being infeasible or suboptimal. Furthermore, we analyze the stability of the resulting estimator with a bounded error in the minimization of the cost function. Since our algorithm does not require the solution of an optimization problem during runtime, state estimates can be generated online almost instantly. Simulation results are presented to show the accuracy and time efficiency of the proposed framework compared to online optimization of moving horizon estimation and Kalman filter. To the best of our knowledge, this is the first learning-based state estimator with feasibility and near-optimality guarantees for linear constrained systems.

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arXiv2022

Optimization Landscape of Gradient Descent for Discrete-time Static Output Feedback

In this paper, we analyze the optimization landscape of gradient descent methods for static output feedback (SOF) control of discrete-time linear time-invariant systems with quadratic cost. The SOF setting can be quite common, for example, when there are unmodeled hidden states in the underlying process. We first establish several important properties of the SOF cost function, including coercivity, L-smoothness, and M-Lipschitz continuous Hessian. We then utilize these properties to show that the gradient descent is able to converge to a stationary point at a dimension-free rate. Furthermore, we prove that under some mild conditions, gradient descent converges linearly to a local minimum if the starting point is close to one. These results not only characterize the performance of gradient descent in optimizing the SOF problem, but also shed light on the efficiency of general policy gradient methods in reinforcement learning.

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