function?[V?policy]?=?mdp_bellman_operator（P?PR?discount?Vprev）


%?mdp_bellman_operator?Applies?the?Bellman?operator?on?the?value?function?Vprev
%??????????????????????Returns?a?new?value?function?and?a?Vprev-improving?policy
%?Arguments?---------------------------------------------------------------
%?Let?S?=?number?of?states?A?=?number?of?actions
%???P（SxSxA）?=?transition?matrix
%??????????????P?could?be?an?array?with?3?dimensions?or?
%??????????????a?cell?array?（1xA）?each?cell?containing?a?matrix?（SxS）?possibly?sparse
%???PR（SxA）?=?reward?matrix
%??????????????PR?could?be?an?array?with?2?dimensions?or?
%??????????????a?sparse?matrix
%???discount?=?discount?rate?in?]0?1]
%???Vprev（S）?=?value?function
%?Evaluation?--------------------------------------------------------------
%???V（S）???=?new?value?function
%???policy（S）?=?Vprev-improving?policy

%?MDPtoolbox:?Markov?Decision?Processes?Toolbox
%?Copyright?（C）?2009??INRA
%?Redistribution?and?use?in?source?and?binary?forms?with?or?without?modification?
%?are?permitted?provided?that?the?following?conditions?are?met:
%????*?Redistributions?of?source?code?must?retain?the?above?copyright?notice?
%??????this?list?of?conditions?and?the?following?disclaimer.
%????*?Redistributions?in?binary?form?must?reproduce?the?above?copyright?notice?
%??????this?list?of?conditions?and?the?following?disclaimer?in?the?documentation?
%??????and/or?other?materials?provided?with?the?distribution.
%????*?Neither?the?name?of?the??nor?the?names?of?its?contributors?
%??????may?be?used?to?endorse?or?promote?products?derived?from?this?software?
%??????without?specific?prior?written?permission.
%?THIS?SOFTWARE?IS?PROVIDED?BY?THE?COPYRIGHT?HOLDERS?AND?CONTRIBUTORS?“AS?IS“?AND?
%?ANY?EXPRESS?OR?IMPLIED?WARRANTIES?INCLUDING?BUT?NOT?LIMITED?TO?THE?IMPLIED?
%?WARRANTIES?OF?MERCHANTABILITY?AND?FITNESS?FOR?A?PARTICULAR?PURPOSE?ARE?DISCLAIMED.
%?IN?NO?EVENT?SHALL?THE?COPYRIGHT?HOLDER?OR?CONTRIBUTORS?BE?LIABLE?FOR?ANY?DIRECT
%?INDIRECT?INCIDENTAL?SPECIAL?EXEMPLARY?OR?CONSEQUENTIAL?DAMAGES?（INCLUDING?
%?BUT?NOT?LIMITED?TO?PROCUREMENT?OF?SUBSTITUTE?GOODS?OR?SERVICES;?LOSS?OF?USE?
%?DATA?OR?PROFITS;?OR?BUSINESS?INTERRUPTION）?HOWEVER?CAUSED?AND?ON?ANY?THEORY?OF?
%?LIABILITY?WHETHER?IN?CONTRACT?STRICT?LIABILITY?OR?TORT?（INCLUDING?NEGLIGENCE?
%?OR?OTHERWISE）?ARISING?IN?ANY?WAY?OUT?OF?THE?USE?OF?THIS?SOFTWARE?EVEN?IF?ADVISED
%?OF?THE?POSSIBILITY?OF?SUCH?DAMAGE.


if?discount?<=?0?|?discount?>?1
?????disp（‘--------------------------------------------------------‘）
?????disp（‘MDP?Toolbox?ERROR:?Discount?rate?must?be?in?]0;?1]‘）
?????disp（‘--------------------------------------------------------‘）
elseif?（（iscell（P））?&?（size（Vprev）?~=?size（P{1}1）））
????disp（‘--------------------------------------------------------‘）
????disp（‘MDP?Toolbox?ERROR:?Vprev?must?have?the?same?dimension?as?P‘）
????disp（‘--------------------------------------------------------‘）
elseif?（（~iscell（P））?&?（size（Vprev）?~=?size（P1）））

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2009-11-09?17:24??MDPtoolbox\
?????文件??????????63??2009-11-09?17:08??MDPtoolbox\AUTHORS
?????文件????????1563??2009-11-09?17:08??MDPtoolbox\COPYING
?????文件????????2437??2009-11-09?17:08??MDPtoolbox\README
?????目錄???????????0??2009-11-09?17:08??MDPtoolbox\documentation\
?????文件????????6876??2009-11-09?17:08??MDPtoolbox\documentation\BIA.png
?????文件????????3110??2009-11-09?17:08??MDPtoolbox\documentation\DOCUMENTATION.html
?????文件??????134450??2009-11-09?17:08??MDPtoolbox\documentation\INRA.png
?????文件?????????231??2009-11-09?17:08??MDPtoolbox\documentation\arrow.gif
?????文件????????6469??2009-11-09?17:08??MDPtoolbox\documentation\index_alphabetic.html
?????文件????????7022??2009-11-09?17:08??MDPtoolbox\documentation\index_category.html
?????文件????????3245??2009-11-09?17:08??MDPtoolbox\documentation\mdp_LP.html
?????文件????????4185??2009-11-09?17:08??MDPtoolbox\documentation\mdp_Q_learning.html
?????文件????????3276??2009-11-09?17:08??MDPtoolbox\documentation\mdp_bellman_operator.html
?????文件????????2959??2009-11-09?17:08??MDPtoolbox\documentation\mdp_check.html
?????文件????????2465??2009-11-09?17:08??MDPtoolbox\documentation\mdp_check_square_stochastic.html
?????文件????????2885??2009-11-09?17:08??MDPtoolbox\documentation\mdp_computePR.html
?????文件????????3357??2009-11-09?17:08??MDPtoolbox\documentation\mdp_computePpolicyPRpolicy.html
?????文件????????3363??2009-11-09?17:08??MDPtoolbox\documentation\mdp_eval_policy_TD_0.html
?????文件????????7506??2009-11-09?17:08??MDPtoolbox\documentation\mdp_eval_policy_iterative.html
?????文件????????2984??2009-11-09?17:08??MDPtoolbox\documentation\mdp_eval_policy_matrix.html
?????文件????????3691??2009-11-09?17:08??MDPtoolbox\documentation\mdp_eval_policy_optimality.html
?????文件????????6834??2009-11-09?17:08??MDPtoolbox\documentation\mdp_example_forest.html
?????文件????????3833??2009-11-09?17:08??MDPtoolbox\documentation\mdp_example_rand.html
?????文件????????4160??2009-11-09?17:08??MDPtoolbox\documentation\mdp_finite_horizon.html
?????文件????????4940??2009-11-09?17:08??MDPtoolbox\documentation\mdp_policy_iteration.html
?????文件????????4966??2009-11-09?17:08??MDPtoolbox\documentation\mdp_policy_iteration_modified.html
?????文件????????7733??2009-11-09?17:08??MDPtoolbox\documentation\mdp_relative_value_iteration.html
?????文件????????2082??2009-11-09?17:08??MDPtoolbox\documentation\mdp_span.html
?????文件????????6731??2009-11-09?17:08??MDPtoolbox\documentation\mdp_value_iteration.html
?????文件????????8689??2009-11-09?17:08??MDPtoolbox\documentation\mdp_value_iterationGS.html
............此處省略27個文件信息