Backup
PURPOSE 
Backupt for a given belief (discrete state version).
SYNOPSIS
function [alpha a v]=Backup(P,b,V,Alphas_j_a_o)
DESCRIPTION
Backupt for a given belief (discrete state version).
Belief backup function for POMDP defined on discrete state spaces.
The backup operator is introduced in Section 4 (page 12) but without any
assumption on the type of state space.
This function basically computes one Alpha-vector for each action and
selects the one that gives higher value for the given belief.
Parameters:
P: The POMDP
b: The belief
V: The previous policy/value function/set of alpha-elements.
Alphas_j_a_o: The set of pre-compute alpha_j_a_o elements. If empty,
the alpha_j_a_o elements are computed on the fly.CROSS-REFERENCE INFORMATION
This function calls:
- Expectation Expectation between a belief and a alpha-element.
- Expectation Expectation between a belief and a alpha-element.
- get Get for GBeliefs.
- Expectation Expectation between a belief and a alpha-element.
- get Get function for the GMixture object.
- get Gaussian object get function.
- get Get function for CS_CO_CA_POMDPs.
- get Get function for CS_CO_DA_POMDPs.
- ComputeAlpha_a Compute the alpha_i_n-element for the given action and belief.
- get Get function for CS_CO_POMDPs.
- get Get function for CS_DO_CA_POMDPs.
- get Get function for CS_DO_DA_POMDPs.
- ComputeAlpha_a Compute the alpha_i_n-element for the given action and belief.
- 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.
- ComputeAlpha_a Compute the alpha_i_n-element for the given action and belief.
- get Get functio for POMDPs.
- dim Dimensionality of a continuous space.
- max Upper bound of a CSpace
- dim Dimensionality of a discrete space.
SOURCE CODE
0001 function [alpha a v]=Backup(P,b,V,Alphas_j_a_o) 0002 % Backupt for a given belief (discrete state version). 0003 % 0004 % Belief backup function for POMDP defined on discrete state spaces. 0005 % The backup operator is introduced in Section 4 (page 12) but without any 0006 % assumption on the type of state space. 0007 % 0008 % This function basically computes one Alpha-vector for each action and 0009 % selects the one that gives higher value for the given belief. 0010 % 0011 % Parameters: 0012 % P: The POMDP 0013 % b: The belief 0014 % V: The previous policy/value function/set of alpha-elements. 0015 % Alphas_j_a_o: The set of pre-compute alpha_j_a_o elements. If empty, 0016 % the alpha_j_a_o elements are computed on the fly. 0017 0018 A=get(P,'ActionSpace'); % This is suposed to be discrete 0019 if isa(A,'CSpace') 0020 error('The Action Space must be discrete at this point'); 0021 end 0022 Elements_a=arrayfun(@(a)(ComputeAlpha_a(P,V,b,a,Alphas_j_a_o)),1:dim(A),'UniformOutput',false); 0023 [v a]=max(cellfun(@(ea)(Expectation(b,ea)),Elements_a)); 0024 alpha=Elements_a{a}; 0025