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.

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.

Addressing Value Estimation Errors in Reinforcement Learning with a State-Action Return Distribution Function

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

Direct and indirect reinforcement learning

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 methods according to how they seek optimal policy of the Markov Decision Process (MDP) problem. The former solves optimal policy by directly maximizing an objective function using gradient descent method, 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 take vanilla policy gradient and approximate policy iteration to study their internal relationship, and reveal that both direct and indirect methods can be unified in actor-critic architecture and are equivalent if we always choose stationary state distribution of current policy as initial state distribution of MDP. Finally, we classify the current mainstream RL algorithms and compare the differences between other criteria including value-based and policy-based, model-based and model-free.

Deep adaptive dynamic programming for nonaffine nonlinear optimal control problem with state constraints

This paper presents a constrained deep adaptive dynamic programming (CDADP) algorithm to solve general nonlinear optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Both the policy and value function are approximated by deep neural networks (NNs), which directly map the system state to action and value function respectively without needing to use hand-crafted basis function. The proposed algorithm considers the state constraints by transforming the policy improvement process to a constrained optimization problem. Meanwhile, a trust region constraint is added to prevent excessive policy update. We first linearize this constrained optimization problem locally into a quadratically-constrained quadratic programming problem, and then obtain the optimal update of policy network parameters by solving its dual problem. We also propose a series of recovery rules to update the policy in case the primal problem is infeasible. In addition, parallel learners are employed to explore different state spaces and then stabilize and accelerate the learning speed. The vehicle control problem in path-tracking task is used to demonstrate the effectiveness of this proposed method.

Generalized Policy Iteration for Optimal Control in Continuous Time

This paper proposes the Deep Generalized Policy Iteration (DGPI) algorithm to find the infinite horizon optimal control policy for general nonlinear continuous-time systems with known dynamics. Unlike existing adaptive dynamic programming algorithms for continuous time systems, DGPI does not require the admissibility of initialized policy, and input-affine nature of controlled systems for convergence. Our algorithm employs the actor-critic architecture to approximate both policy and value functions with the purpose of iteratively solving the Hamilton-Jacobi-Bellman equation. Both the policy and value functions are approximated by deep neural networks. Given any arbitrary initial policy, the proposed DGPI algorithm can eventually converge to an admissible, and subsequently an optimal policy for an arbitrary nonlinear system. We also relax the update termination conditions of both the policy evaluation and improvement processes, which leads to a faster convergence speed than conventional Policy Iteration (PI) methods, for the same architecture of function approximators. We further prove the convergence and optimality of the algorithm with thorough Lyapunov analysis, and demonstrate its generality and efficacy using two detailed numerical examples.

Intention-aware Long Horizon Trajectory Prediction of Surrounding Vehicles using Dual LSTM Networks

As autonomous vehicles (AVs) need to interact with other road users, it is of importance to comprehensively understand the dynamic traffic environment, especially the future possible trajectories of surrounding vehicles. This paper presents an algorithm for long-horizon trajectory prediction of surrounding vehicles using a dual long short term memory (LSTM) network, which is capable of effectively improving prediction accuracy in strongly interactive driving environments. In contrast to traditional approaches which require trajectory matching and manual feature selection, this method can automatically learn high-level spatial-temporal features of driver behaviors from naturalistic driving data through sequence learning. By employing two blocks of LSTMs, the proposed method feeds the sequential trajectory to the first LSTM for driver intention recognition as an intermediate indicator, which is immediately followed by a second LSTM for future trajectory prediction. Test results from real-world highway driving data show that the proposed method can, in comparison to state-of-art methods, output more accurate and reasonable estimate of different future trajectories over 5s time horizon with root mean square error (RMSE) for longitudinal and lateral prediction less than 5.77m and 0.49m, respectively.

Indirect Shared Control of Highly Automated Vehicles for Cooperative Driving between Driver and Automation

It is widely acknowledged that drivers should remain in the control loop of automated vehicles before they completely meet real-world operational conditions. This paper introduces an `indirect shared control' scheme for steer-by-wire vehicles, which allows the vehicle control authority to be continuously shared between the driver and automation through unphysical cooperation. This paper first balances the control objectives of the driver and automation in a weighted summation, and then models the driver's adaptive control behavior using a predictive control approach. The driver adaptation modeling enables off-line evaluations of indirect shared control systems and thus facilitates the design of the assistant controller. Unlike any conventional driver model for manual driving, this model assumes that the driver can learn and incorporate the controller strategy into his internal model for more accurate path following. To satisfy the driving demands in different scenarios, a sliding-window detector is designed to continuously monitor the driver intention and automatically switch the authority weights between the driver and automation. The simulation results illustrate the advantages of considering the driver adaptation in path-following and obstacle-avoidance tasks, and show the effectiveness of indirect shared control for cooperative driving.