===== Task11 - Greedy policy in pursuit-evasion ======
The main task is to implement a simple $\epsilon$-greedy policy for robotics pursuit-evasion game.

|**Deadline**  |  15. December 2018, 23:59 PST |
|**Points**  |  3 |
|**Label in BRUTE**  |  Task11 |
|**Files to submit**  |  archive with ''player''|
| |  <fc #ff0000>Minimal content of the archive:</fc> ''player/Player.py''| 
|**Resources**  |  {{ :courses:b4m36uir:hw:task11.zip |Task11 resource files}}|

===Assignment===
In file ''player/Player.py'' in function ''greedy_policy'' implement the $\epsilon$-greedy policy decision making for pursuit-evasion game.
The pursuit-evasion problem is a problem in computer science where a set of pursuers is trying to catch a set of evaders.\\
{{:courses:b4m36uir:labs:pursuit-evaision.png?200|}}

In greedy policy, the next-best state is selected in each discrete step of the game simulation without considering longer prediction horizon.\\
Usual policies incorporate distances between individual agents as follows:\\ 
  * **For evaders select the most distant node to the pursuers**
  * **For pursuers select the closest node to the closest evader**

In $\epsilon$-greedy policy, the $\epsilon$ parameter gives the probability, with which the robot selects the next-step according to the above strategy. I.e., when $\epsilon=1$ the robot selects the next step according to the rules described above, when $\epsilon=0$ the robot selects its next step randomly. 

In each step of the game, the player has to move all its robots for a single step (4-neighborhood).

The ''greedy_policy'' function has the following prescription:<code python>
    def greedy_policy(self, gridmap, evaders, pursuers, epsilon=1):
        """
        Method to calculate the greedy policy action
        
        Parameters
        ----------
        gridmap: GridMap
            Map of the environment
        evaders: list((int,int))
            list of coordinates of evaders in the game (except the player's robots, if he is evader)
        pursuers: list((int,int))
            list of coordinates of pursuers in the game (except the player's robots, if he is pursuer)
        epsilon: float (optional)
            optional epsilon-greedy parameter
        """
</code>

The purpose of the function is to internally update the ''self.next_robots'' variable, which is a list of ''(int, int)'' robot coordinates based on the current state of the game, given ''gridmap'' grid map of the environment and the player's role ''self.role''. The player is given the list ''evaders'' of all evading robots in the game other than his robots and the list of ''pursuers'' of all pursuing robots in the game other than his robots. I.e., the complete set of robots in game is given as the union of ''evaders'', ''pursuers'' and ''self.robots''.\\

During the gameplay, each player is asked to update their intention for the next move coded in the ''self.next_robots'' variable by calling the ''calculate_step'' function. Afterward, the step is performed by calling the ''take_step̈́'' function followed by the game checking each step, whether it complies to the rules of the game.

The game ends after a predefined number of steps or when all the evaders are captured.

=== Approach ===
The recommended approach to the $\epsilon$-greedy policy implementation is following:
  * For each robot evaluate its options of movement and select the best one (given the $\epsilon$ parameter)
    * If the player's role is pursuer, calculate the distance from each option to each evader 
    * If the player's role is evader, calculate the distance from each option to each pursuer
    * The distance is given as the number of steps between the position of evader/pursuer and the optional position of the robot. For that you may use the ''GridPlanner'' class utilized in the previous tasks. In fact, as we are only interested in the number of steps between two poses, it is recommended to use the implementation of the Floyd-Warshall with lazy initialization to precompute the distances, which significantly speeds-up the player's decision and also improves the results of the Monte-Carlo Tree Search policy ([[courses:b4m36uir:hw:task12|Task12]])
    * Based on the player's role, select the best option with $\epsilon$ probability. Note, the evaders select the most distant node to the pursuers and pursuers select the closest node to the closest evader.

=== Evaluation === 
The correctness of the greedy approach can be well checked with ''pacman_1.game'' which is shown in the following figure\\
{{:courses:b4m36uir:hw:pursuit_pacman.png?200|}}

The decision of the pursuers is straight-forward; however, the correctness of the evader decision can be checked. Note, the evader selects the most distant node to the closest pursuer. If you select the closest node to all pursuers, the robot will directly intercept the pursuer to the left.