SampleBeliefs
PURPOSE 
Samples a set of beliefs from a POMDP.
SYNOPSIS
function SB=SampleBeliefs(P,start,nBeliefs,minBeliefDist,stepsXtrial,minR,maxR)
DESCRIPTION
Samples a set of beliefs from a POMDP.
Defines a set of 'nBeliefs' beliefs randomly simulating a POMDP.
This function corresponds to that in line 2 of Table 2 in section 6 of
the paper.
The sampling of beliefs is organized in trials. Each trial starts from
the given 'start' belief and evolves selecting actions and observations
at radom. Actions are selected with uniform probability and
observations from the corresponding observation model.
Each trial is stopped after executing 'stepsXtrial' steps of when the
received reward is outside the interval [minR, maxR].
Only beliefs that are further away more than 'minBelifDist' from any
other already stored beliefs are considered.
The sampling of beliefs can be quite slow and some information is
printed while it proceeds.
'.' Means a new belief has been added to the output.
'*' Means a trial has ended.
See also SimulationStep, @DBelief/distance, @GMixture/Distance,
@PBelief/Distance.CROSS-REFERENCE INFORMATION
This function calls:
- Distance Distance between beliefs.
- rand Random state from a discrete belief.
- get Get for GBeliefs.
- Distance Distance between beliefs.
- rand Random state from a belief.
- Crop Limits all means to be inside the given space.
- Distance Approximated Kullback-Leibler distance between Gaussian mixture.
- get Get function for the GMixture object.
- rand Generates random points on a GMixture.
- Crop Forces the Gaussian mean to be in a given space.
- get Gaussian object get function.
- rand Generates random ponts on a Gaussian.
- get Get function for CS_CO_CA_POMDPs.
- get Get function for CS_CO_DA_POMDPs.
- get Get function for CS_CO_POMDPs.
- get Get function for CS_DO_CA_POMDPs.
- get Get function for CS_DO_DA_POMDPs.
- get Get function for CS_POMDPs.
- get Get function for DS_CO_CA_POMDPs.
- get Get function for DS_CO_DA_POMDPs.
- get Get function for DS_DO_CA_POMDPs.
- get Get function for DS_DO_DA_POMDPs.
- SimulationStep Executes one step of a POMDP simulation.
- get Get functio for POMDPs.
- Crop Forces a state to be in a given continuous sub-space.
- min Lower bound of a CSpace
- rand Random state from a continuous space.
- Crop Forces a state to be in a given discrete space.
- rand Random state from a discrete space.
- GenerateFigure5Data Generates the data for Figure 5.
- GenerateFigure7aData Generates the data for Figure 7-left.
- TestOne Samples beliefs and executes Perseus on a given problem.
- TestRep Executes many times of Perseus on a given problem.
SOURCE CODE
0001 function SB=SampleBeliefs(P,start,nBeliefs,minBeliefDist,stepsXtrial,minR,maxR) 0002 % Samples a set of beliefs from a POMDP. 0003 % 0004 % Defines a set of 'nBeliefs' beliefs randomly simulating a POMDP. 0005 % This function corresponds to that in line 2 of Table 2 in section 6 of 0006 % the paper. 0007 % 0008 % The sampling of beliefs is organized in trials. Each trial starts from 0009 % the given 'start' belief and evolves selecting actions and observations 0010 % at radom. Actions are selected with uniform probability and 0011 % observations from the corresponding observation model. 0012 % Each trial is stopped after executing 'stepsXtrial' steps of when the 0013 % received reward is outside the interval [minR, maxR]. 0014 % 0015 % Only beliefs that are further away more than 'minBelifDist' from any 0016 % other already stored beliefs are considered. 0017 % 0018 % The sampling of beliefs can be quite slow and some information is 0019 % printed while it proceeds. 0020 % '.' Means a new belief has been added to the output. 0021 % '*' Means a trial has ended. 0022 % 0023 % See also SimulationStep, @DBelief/distance, @GMixture/Distance, 0024 % @PBelief/Distance. 0025 0026 rand('state',sum(100*clock)); 0027 0028 A=get(P,'ActionSpace'); 0029 S=get(P,'StateSpace'); 0030 0031 md=minBeliefDist+1; 0032 SB=cell(1,nBeliefs); 0033 k=0; 0034 r=maxR-1; 0035 while k<nBeliefs 0036 if (mod(k,stepsXtrial)==0) || (r>maxR) || (r<minR) 0037 b=start; 0038 s=Crop(S,rand(b)); 0039 0040 fprintf('*\n'); 0041 end 0042 a=rand(A); 0043 [s b o r]=SimulationStep(P,b,s,a); 0044 0045 if (k>1) && (minBeliefDist>0) 0046 md=min(cellfun(@(b1)(Distance(b,b1)),SB(1,k))); 0047 end 0048 if md>minBeliefDist 0049 k=k+1; 0050 SB{k}=b; 0051 0052 fprintf('.'); 0053 if mod(k,80)==0 0054 fprintf('\n'); 0055 end 0056 end 0057 end 0058 fprintf('\n'); 0059