Model-based Safe Reinforcement Learning using Generalized Control Barrier Function

Model information can be used to predict future trajectories, so it has huge potential to avoid dangerous region when implementing reinforcement learning (RL) on real-world tasks, like autonomous driving. However, existing studies mostly use model-free constrained RL, which causes inevitable constraint violations. This paper proposes a model-based feasibility enhancement technique of constrained RL, which enhances the feasibility of policy using generalized control barrier function (GCBF) defined on the distance to constraint boundary. By using the model information, the policy can be optimized safely without violating actual safety constraints, and the sample efficiency is increased. The major difficulty of infeasibility in solving the constrained policy gradient is handled by an adaptive coefficient mechanism. We evaluate the proposed method in both simulations and real vehicle experiments in a complex autonomous driving collision avoidance task. The proposed method achieves up to four times fewer constraint violations and converges 3.36 times faster than baseline constrained RL approaches.

Recurrent Model Predictive Control

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.

Mixed Policy Gradient

Reinforcement learning (RL) has great potential in sequential decision-making. At present, the mainstream RL algorithms are data-driven, relying on millions of iterations and a large number of empirical data to learn a policy. Although data-driven RL may have excellent asymptotic performance, it usually yields slow convergence speed. As a comparison, model-driven RL employs a differentiable transition model to improve convergence speed, in which the policy gradient (PG) is calculated by using the backpropagation through time (BPTT) technique. However, such methods suffer from numerical instability, model error sensitivity and low computing efficiency, which may lead to poor policies. In this paper, a mixed policy gradient (MPG) method is proposed, which uses both empirical data and the transition model to construct the PG, so as to accelerate the convergence speed without losing the optimality guarantee. MPG contains two types of PG: 1) data-driven PG, which is obtained by directly calculating the derivative of the learned Q-value function with respect to actions, and 2) model-driven PG, which is calculated using BPTT based on the model-predictive return. We unify them by revealing the correlation between the upper bound of the unified PG error and the predictive horizon, where the data-driven PG is regraded as 0-step model-predictive return. Relying on that, MPG employs a rule-based method to adaptively adjust the weights of data-driven and model-driven PGs. In particular, to get a more accurate PG, the weight of the data-driven PG is designed to grow along the learning process while the other to decrease. Besides, an asynchronous learning framework is proposed to reduce the wall-clock time needed for each update iteration. Simulation results show that the MPG method achieves the best asymptotic performance and convergence speed compared with other baseline algorithms.

Separated Proportional-Integral Lagrangian for Chance Constrained Reinforcement Learning

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.

Steadily Learn to Drive with Virtual Memory

Reinforcement learning has shown great potential in developing high-level autonomous driving. However, for high-dimensional tasks, current RL methods suffer from low data efficiency and oscillation in the training process. This paper proposes an algorithm called Learn to drive with Virtual Memory (LVM) to overcome these problems. LVM compresses the high-dimensional information into compact latent states and learns a latent dynamic model to summarize the agent's experience. Various imagined latent trajectories are generated as virtual memory by the latent dynamic model. The policy is learned by propagating gradient through the learned latent model with the imagined latent trajectories and thus leads to high data efficiency. Furthermore, a double critic structure is designed to reduce the oscillation during the training process. The effectiveness of LVM is demonstrated by an image-input autonomous driving task, in which LVM outperforms the existing method in terms of data efficiency, learning stability, and control performance.

Model-Based Actor-Critic with Chance Constraint for Stochastic System

Safety constraints are essential for reinforcement learning (RL) applied in real-world situations. Chance constraints are suitable to represent the safety requirements in stochastic systems. Most existing RL methods with chance constraints have a low convergence rate, and only learn a conservative policy. In this paper, we propose a model-based chance constrained actor-critic (CCAC) algorithm which can efficiently learn a safe and non-conservative policy. Different from existing methods that optimize a conservative lower bound, CCAC directly solves the original chance constrained problems, where the objective function and safe probability is simultaneously optimized with adaptive weights. In order to improve the convergence rate, CCAC utilizes the gradient of dynamic model to accelerate policy optimization. The effectiveness of CCAC is demonstrated by an aggressive car-following task. Experiments indicate that compared with previous methods, CCAC improves the performance by 57.6% while guaranteeing safety, with a five times faster convergence rate.

Ternary Policy Iteration Algorithm for Nonlinear Robust Control

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.

Safe Reinforcement Learning for Autonomous Vehicles through Parallel Constrained Policy Optimization

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.

Mixed Reinforcement Learning with Additive Stochastic Uncertainty

Reinforcement learning (RL) methods often rely on massive exploration data to search optimal policies, and suffer from poor sampling efficiency. This paper presents a mixed reinforcement learning (mixed RL) algorithm by simultaneously using dual representations of environmental dynamics to search the optimal policy with the purpose of improving both learning accuracy and training speed. The dual representations indicate the environmental model and the state-action data: the former can accelerate the learning process of RL, while its inherent model uncertainty generally leads to worse policy accuracy than the latter, which comes from direct measurements of states and actions. In the framework design of the mixed RL, the compensation of the additive stochastic model uncertainty is embedded inside the policy iteration RL framework by using explored state-action data via iterative Bayesian estimator (IBE). The optimal policy is then computed in an iterative way by alternating between policy evaluation (PEV) and policy improvement (PIM). The convergence of the mixed RL is proved using the Bellman's principle of optimality, and the recursive stability of the generated policy is proved via the Lyapunov's direct method. The effectiveness of the mixed RL is demonstrated by a typical optimal control problem of stochastic non-affine nonlinear systems (i.e., double lane change task with an automated vehicle).

Distributional Soft Actor-Critic: Off-Policy Reinforcement Learning for Addressing Value Estimation Errors

In current reinforcement learning (RL) methods, function approximation errors are known to lead to the overestimated or underestimated Q-value estimates, thus resulting in suboptimal policies. We show that the learning of a state-action return distribution function can be used to improve the Q-value estimation accuracy. We employ the return distribution function within the maximum entropy RL framework in order to develop what we call the Distributional Soft Actor-Critic (DSAC) algorithm, which is an off-policy method for continuous control setting. Unlike traditional distributional RL algorithms which typically only learn a discrete return distribution, DSAC directly learns a continuous return distribution by truncating the difference between the target and current distribution to prevent gradient explosion. Additionally, we propose a new Parallel Asynchronous Buffer-Actor-Learner architecture (PABAL) to improve the learning efficiency, which is a generalization of current high-throughput learning architectures. We evaluate our method on the suite of MuJoCo continuous control tasks, achieving state-of-the-art performance.