## 1 Introduction  
Ride quality and passenger comfort are some of the major concerns of any vehicle designer and have been well investigated and researched over the past few decades. The vehicle suspension system plays an important role in vehicle safety, handling, and comfort. It keeps the tires in contact with the road, provides good handling and stable steering, and minimizes the vibrations and oscillations due to road irregularities, which ensure the comfort of the passengers. In general, the suspension is divided into three types: passive, semi-active, and active suspension systems. Most of today's vehicles use the passive system, which consists of a spring and a damper that are fixed at the design stage, which provide an acceptable performance for a limited frequency range. Changing the suspension properties like the damping coefficient allows for good performance, but in a different frequency range. That is why sport cars have better handling than standard cars, whereas the latter have better riding quality. In a semi-active suspension system, energy is not added to the system; however, the system varies the viscous damping co-efficient of the shock absorber. Therefore, the need for a system that attains the objectives for the entire working frequency range justifies the momentum for active suspension research. In the active suspension system, an actuator is added to the spring and damper, which adds energy to the system by exerting an adaptive counter force, resulting in an improved dynamics behavior. Several controllers were implemented in the active suspension system problem, and the discrete indirect pole assignment with a fuzzy logic gain scheduler was developed by [1]. A non-linear model of the active suspension was investigated by [2] using a sliding mode controller that utilizes the sky-hook damper system without the need for road profile input. There have been more recent attempts to improve the system such as the study conducted by [3], which used two loop PID applied to the half model in the non-linear form. Compared to the passive system with the same parameters, they showed excellent improvement. However, the controller could not completely reject the disturbance. Another example of the utilization of the PID controller in the half model was that developed by [4]. They studied three scenarios and tried three tuning methods where the iterative learning algorithm performed better than the other two methods. Reference [5] showed that fuzzy logic performed significantly better than the PID in the quarter model based on two types of road conditions. Another comparison based on the quarter model, but between a robust PI and Linear Quadratic Regulator (LQR) controller, was conducted by [6], where they showed that the LQR outperformed the PI controller in the presence of parameter uncertainty. Another optimal controller is \(H_{\infty}\), which was examined by [7] and showed a 93% reduction in the car's acceleration, wheel travel, and suspension travel. Recently, machine learning has been widely investigated in control problems and applied to vehicle suspension. In many cases, neural networks are used in combination with traditional controllers including the sliding mode controller [8], PID [9], and LQR [10] to enhance the controller performance and other tasks like determining the road roughness [11], but they have rarely been used as the controller itself. A good example that motivates the use of machine learning methods as the controller is [12], where a neural network was trained by the optimal PID and surpassed it under parameter uncertainties. Another machine learning method that has recently gained momentum and shown great success in a broad range of applications including games and economics, but rarely applied to control problems, is reinforcement learning. Despite the rare application of reinforcement learning in the active suspension problem, one of the earliest attempts to the best of our knowledge was conducted by [13; 14; 15].