In　this　paper,　a　novel　policy　iteration　adaptive　dynamic　programming　(ADP)　algorithm　is　presented　which　is　called　＂local　policy　iteration　ADP　algorithm＂　to　obtain　the　optimal　control　for　discrete　stochastic　processes.　In　the　proposed　local　policy　iteration　ADP　algorithm,　the　iterative　decision　rules　are　updated　in　a　local　space　of　the　whole　state　space.　Hence,　we　can　significantly　reduce　the　computational　burden　for　the　CPU　in　comparison　with　the　conventional　policy　iteration　algorithm.　By　analyzing　the　convergence　properties　of　the　proposed　algorithm,　it　is　shown　that　the　iterative　value　functions　are　monotonically　nonincreasing.　Besides,　the　iterative　value　functions　can　converge　to　the　optimum　in　a　local　policy　space.　In　addition,　this　local　policy　space　will　be　described　in　detail　for　the　first　time.　Under　a　few　weak　constraints,　it　is　also　shown　that　the　iterative　value　function　will　converge　to　the　optimal　performance　index　function　of　the　global　policy　space.　Finally,　a　simulation　example　is　presented　to　validate　the　effectiveness　of　the　developed　method.