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Learning to Drive Via Apprenticeship Learning and Deep Reinforcement Learning

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Learning to Drive Via Apprenticeship Learning and Deep Reinforcement Learning Learning to Drive via Apprenticeship Learning and Deep Reinforcement Learning 1st Wenhui Huang 2nd Francesco Braghin 3rd Zhuo Wang Industrial and Information Engineering Industrial and Information Engineering School of communication engineering Politecnico Di Milano Politecnico Di Milano Xidian University Milano, Italy Milano, Italy XiAn, China [email protected] [email protected] zwang [email protected] Abstract—With the implementation of reinforcement learning the reward function is tough to be hand-made directly. To (RL) algorithms, current state-of-art autonomous vehicle technol- overcome this problem, [8] proposed apprenticeship learning ogy have the potential to get closer to full automation. However, via inverse reinforcement learning (IRL) approach . IRL aims most of the applications have been limited to game domains or discrete action space which are far from the real world at recovering the unknown reward function by observing driving. Moreover, it is very tough to tune the parameters of expert demonstration. reward mechanism since the driving styles vary a lot among Both forward driving and stopping under the traffic rules the different users. For instance, an aggressive driver may are frequent behaviors in real life driving. However, recent prefer driving with high acceleration whereas some conservative studies [9], [10] are only focusing on obstacle avoidance and drivers prefer a safer driving style. Therefore, we propose an apprenticeship learning in combination with deep reinforcement there is no research on learning forward driving and stopping learning approach that allows the agent to learn the driving behaviors by considering traffic rules via reinforcement learn- and stopping behaviors with continuous actions. We use gradient ing techniques. In this paper, we addressed above problem by inverse reinforcement learning (GIRL) algorithm to recover the means of apprenticeship learning in combination with DRL unknown reward function and employ REINFORCE as well as approach. More specifically, we implemented gradient inverse Deep Deterministic Policy Gradient algorithm (DDPG) to learn the optimal policy. The performance of our method is evaluated reinforcement learning (GIRL) algorithm [11] to recover the in simulation-based scenario and the results demonstrate that unknown reward funciton and employed DDPG algorithm in the agent performs human like driving and even better in some order to train the agent to drive by keeping traffic rules and aspects after training. stop in front of the stop sign autonomously. Furthermore, Index Terms—Reinforcement Learning Application, Inverse REINFORCE algorithm is employed in RL step as well in Reinforcment Learning, Autonomous Driving order to compare the performance with DDPG algorithm. I. INTRODUCTION II. RELATED WORKS Recent studies indicate that the interest in applying robotics At the early state, researchers tried to exploit Aritifical and autonomous system to real life is growing dramatically [1], Neural Networks as the controller of the taking action. One [2]. Especially, the pace of techinical upgrading and innovation of the typical paper is ALVINN [12]. The paper proposed for autonomous vehicle driving is accelerating a lot [3] and this a 3-layers back-propagation network to complete the task of is mostly thanks to the capability of the machine learning(ML). road following. The network takes images from camera as the Reinforcement learning (RL), as one branch of the ML, is inputs, passing through 29 hidden layers, and produces the the most widely used technique in sequential decision making direction of the vehicle should travel along the road as the arXiv:2001.03864v1 [cs.RO] 12 Jan 2020 problem. RL can learn the optimal policy through a process output. After certain episodes of the training, the car could by interacting with unknown environment. RL algorithms have navigate successfully along the road . been successfully applied to the autonomous driving in recent One of the more advanced appliations is utilizing DL years [4], [5]. However, these applications are not only limited technique-convolutional neural networks (CNNs) with Dave2- to the discrete aciton problems but also suffer from ”curse of system which was exactly implemented in [13]. Dave2-system dimensionality” once the action extends to continuous state is an end-to-end system which is inspired from ALVINN. The space. In order to solve large continuous state space problem, CNN network in this paper consists of 9 layers, including deep learning (DL) has been implemented in RL, yielding a normalization layer, 5 convolutional layers and 3 fully deep reinforcement learning (DRL) [6]. In recent study, the connected layers . A recent paper [14] employed CNNs to Deep Deterministic Policy Gradient (DDPG) algorithm which the motion planning layer as well. belongs to DRL family, has been successfully applied to target Although utilizing the DL algorithm directly as the con- following control [7]. troller of the behavior seems good enough to achieve the target, One of the issues in RL is the reward function. Knowing it belongs to the behavior cloning which means it only has that autonomous vehicle driving is not a trivial problem, knowledge about the observed data. This kind of approach can only be acceptable under a good hypothesis as well as III. PRELIMINARIES good data including all of the possible cases. A. Background To avoid falling into behavior cloning class, the vehicle A Markov decision process (MDP) is defined by a tuple, should explore and exploit behavior by itself in unknown denoted as M = fS; A; P; R; γg, where S is state space; A environment and the approach that is able to handle this case is is action space; P is transition probability. It stands for the Reinforcement Learning. Reinforcement Learning is learning 0 probability of the transition from state s to s upon taking what to do-how to map situations to actions-so as to maximize action a 2 A; R : S!A is the reward (function), it a numeral reward [15]. In [16] a deep Q-network (DQN) indicates how good the action a 2 A executed from state algorithm is utilized as a decision maker. By passing through s 2 S is; And γ is discount factor which is limited in the the network with 84 by 84 images, three discrete actions, faster range of [0,1). The policy π characterizes the agent’s action and faster-left as well as faster-right, are returned by the frame. in MDP problem. More formally, the policy is a mapping Different from previous paper, [17] employed dynamic model from given states to probabilities of selecting each possible rather than kinematic with same DQN algorithm. However, action:π(a j s) = P(a = A j s = S ). The expected retrun both of the applications are still limited to the discrete action t t based on the state s following the policy π is defined as Value space. funciton, also called state value function, denoted as V (s). In Being aware that driving in real life could not be achieved π RL, we formalize it in mathematical way: with several discrete actions, researchers turn to develope continuous control algorithms. One of the popular algorithms 1 that can handle continuous action space problem is Actor- X V (s) = E [R j S = s] = E γkr j S = s Critic(AC). A paper [18] from Berkeley university evaluated π π t t π t+k+1 t k=0 AC algorithm on the classic cart-pole balancing problem, (1) as well as 3D robots by tuning with bias and variance. Note that in case of terminating state, the value will be 0 Considering the complexity of sampling and diverse problem always. Similarly, the expected return taking action a at state s of AC, Google Deepmind team published a new upgraded AC following policy π is defined as Q function, denoted Qπ(s; a). algorithm-DDPG [6] in 2016. The paper indicates that DDPG The Q funciton can be formalized as: can learn competitive policies using low dimentional observa- tions with only a straightforward actor-critic architecture. 1 X k In RL, the reward function plays a significant role since Qπ(s; a) = Eπ γ rt+k+1 j St = s; At = a (2) the agent is aiming at getting higher reward whenever it k=0 achieves the goal. A classic paper [8] published by Standford Furthermore, Many approaches in reinforcement learning university proposed IRL algorithm to recover the unknown make use of the recursive relationship known as the Bellman reward function based on expert’s demonstration. Apprentice- equation: ship learning has been successfully applied to autonomous vehicles such as learning to drive by maximum entropy IRL Qπ = E rt+1 + γQπ(St+1;At+1) j St = s; At = a (3) [19] and projection-based IRL [5]. The bottleneck of the above B. Gradient Inverse Reinforcement Learning mentioned methods is the requirement of solving multiple forward RL problems iteratively. A new IRL algorithm stated The logic behind the GIRL algorithm is to find out the in [11] is gradient inverse reinforcement leanring (GIRL). The reward function by minimizing the gradient of a parameterized idea is to find the reward function that minimizes the gradient representation of the expert’s policy. In particular, when the of a parameterized representation of the expert’s policy based reward function can be represented by linear combination with on assumption of reward function is in linear combination with the reward features, the minimization can be solved effectively reward features. with optimization method. Under the assumption of linear In this paper, we recover the reward function by means combination, it is possible to formalize the reward in the of GIRL algorithm and implement DDPG algorithm to learn following way: the optimal policy based on the recovered reward function. T REINFORCE algorithm is employed in RL part as well to r!(s; a) = ' (s)! (4) compare the performance with DDPG algirithm.
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