Approach 1 :
 
After a number of empirical tests for same serve and same bat position the parameters for learning were optimised.
• The learning rate was increased from 0.7 to 0.9 and faster learning was observed
• The back propogation learning rate  for the weights in hidden layer was changed from 0.05 to 0.01
• The action set was increased from 8 to 27 and better results were obtained in second case.


In the following observations, the serves were of different types -
 

• A cross-court serve towards the racquet  (=> starting from the oppoisite court of the racquet ) .The ball starting position is low and at a  relatively higher speed .
• A cross-court serve away from the racquet (=> starting from the same court as racquet ). The initial ball position is low and high speed.
Also note that serves 1 and 2 are similar in the sense that they are directed in the same court. Similary serves 3 and 4 are similar.

Other Observations

• The absolute success rate is higher for the serves which naturally come closer to the initial bat position. The success rate is highest for serve 1 followed by serve 2. The serve 1 is slower and hence gives greater time to adjust.
• When a combination of two or more serves is taken the absolute success rate is higher for a combination of similar serves. The  best combinations are (1,2) and (3,4).
• When a combination of two or more serves is taken the success displays show that the success for the same serve/ similar serves  come as bunched together.


Learning Rate
 

• Now we display a few learning curves. In all the curves shown below - the x axis is the number of trials. The trials are over a period of 1000 to 100,000 runs with certain intervals . The y-axis is the number of successful shots in that interval.
• The different colors in the graph distinguish successful shots (=> reaching the ball but playing a wrong shot) from  completely  successful shots (=> hitting a correct shot as well).
 
• CURVE 1 ( Learning rates - 3 successive runs of 20000 trials each)
• CURVE2 (Comparative learning rates - action set size is 8 and 27)
• CURVE3  ( 1 run  of 20000 trials on 2 services selected randomly)
• CURVE4  ( 1 run of 30000  trials on 4 services  selected at random)

 
• Details about the various learning curves are provided alongwith the  images

Approach II

In the following observations, the serves were of different types -
 
• A down the line serve  towards the racquet (=> starting from the same court as racquet) .  The ball starting position is high and the speed is moderate.
• A  lobbed cross-court serve away fom the racquet (=> starting from the same court as racquet). The initial ball postion is high and the speed is slow.
Observations & Conclusions
 
• Nature of solution - The racquet motion is absolutely continuous without any  jerks . Remember that the change in racquet position is due to velocity increments .
• The shot that is played has the bat moving at a velocity with which it approaches the ball just before intersecting its trajectory.
• Learning rate is high for the intermediate success - intercepting the ball
• However rate of learning for total success - landing the ball correctly  is lower  as observed.
• There is a mild fluctuation in the results at times.
Learning Rate
 
• Now we display a few learning curves. In all the curves shown below - the x axis is the number of trials. The trials are over a period of 1000 runs to 100,000 runs with  certain intervals. The y-axis is the number of successful shots  in that interval.

• CURVE1 (1 run of 30000 trials- same serve)
• CURVE2 (1 run - 20000 trials -''  , erroneous case)
• CURVE3 (1 run of 100000 trials - diff reward func)
• CURVE4 (short run of 10000 trials shows fluctuation)
• CURVE5 (3 successive runs of 10000 trials each )
• CURVE6 (3 successive short runs of 1000 trials each )

 
• Details about the various learning curves are provided alongwith the  images

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