it can improve in situations where an analytic model is hard or missing. For the Ball-Paddle system, an analytic model can be derived for the reflection of the ball on the paddle. This model makes a basic assumption that the velocity of the ball, when hitting the paddle, will be reflected along the normal direction of the paddle. Some energy will be absorbed by the paddle and the exact amount is determined by a coefficient of restitution. This coefficient can be measured by bouncing the ball on the paddle while it is flat and observing the successive heights that the ball will reach.

This model seems reasonable according to basic laws of physics and can be tuned carefully by measuring its physical constants. However, this model makes errors in the direction and speed of the reflected ball as it does not exactly follow the assumptions made. This can lead to errors in the controller. Fig. \[fig:analyticvslearned\] shows the path taken by the controller using both the learned model and analytic model. The analytic model overcompensates for the errors it makes and becomes unstable, while the learned model reaches the target location.

![**Imitation policy**. The position of both the ball and 