DiscretizeActionModel

 Discretizes the action space DS_DO_CA_POMDP.

   Discretizes the action space of a DS_DO_CA_POMDP and returns a 
   DS_DO_DA_POMDP.
   The discretization affects the action space, the action model,
   and reward model.
   This function is used in Perseus (and iPerseus) in order to define a
   POMDP with a discre action set so that the normal backup can be executed
   without any issue. The discretization is 'belief' based (different for
   each belief and it is executed just before the backup). 
   The parameter 'optimalAction' is the optimal action for the belief in the
   previous Perseus iteration. In the current implementation, this action
   is added to the discrete set of actions.
   Parameter 'iteration' is the current Perseus (or iPerseus) iteration. 
   Right now the discretization is done sampling uniformly, but could also
   progressively focus toward the optimal action as 'iteration' increases.

   Parameters:
     CA_POMDP: The DS_DO_CA input POMDP.
     optimalAction: The previous optimal action .
     iteration: Current iteration (not used in this implementation).

   See also Perseus, iPerseus.

0001 function DA_POMDP=DiscretizeActionModel(CA_POMDP,optimalAction,iteration)
0002 % Discretizes the action space DS_DO_CA_POMDP.
0003 %
0004 %   Discretizes the action space of a DS_DO_CA_POMDP and returns a
0005 %   DS_DO_DA_POMDP.
0006 %   The discretization affects the action space, the action model,
0007 %   and reward model.
0008 %   This function is used in Perseus (and iPerseus) in order to define a
0009 %   POMDP with a discre action set so that the normal backup can be executed
0010 %   without any issue. The discretization is 'belief' based (different for
0011 %   each belief and it is executed just before the backup).
0012 %   The parameter 'optimalAction' is the optimal action for the belief in the
0013 %   previous Perseus iteration. In the current implementation, this action
0014 %   is added to the discrete set of actions.
0015 %   Parameter 'iteration' is the current Perseus (or iPerseus) iteration.
0016 %   Right now the discretization is done sampling uniformly, but could also
0017 %   progressively focus toward the optimal action as 'iteration' increases.
0018 %
0019 %   Parameters:
0020 %     CA_POMDP: The DS_DO_CA input POMDP.
0021 %     optimalAction: The previous optimal action .
0022 %     iteration: Current iteration (not used in this implementation).
0023 %
0024 %   See also Perseus, iPerseus.
0025 
0026   S=get(CA_POMDP,'StateSpace');
0027   A=Discretize(CA_POMDP.A,CA_POMDP.nSampledActions-1,{optimalAction});
0028   O=get(CA_POMDP,'ObsSpace');
0029   
0030   AM=DiscretizeActionModel(CA_POMDP.DS_CA_ActionModel,A);
0031   OM=get(CA_POMDP,'ObsModel');
0032   RM=DiscretizeRewardModel(CA_POMDP.DS_CA_RewardModel,A);
0033   
0034   name=get(CA_POMDP,'name');
0035   gamma=get(CA_POMDP,'gamma');
0036   
0037   DA_POMDP=DS_DO_DA_POMDP(name,S,A,O,AM,OM,RM,gamma);
0038