Adaptive　critic　technology　has　been　widely　employed　to　solve　the　optimal　control　problems　of　complicated　nonlinear　systems,　but　there　are　some　limitations　to　solve　the　infinite-horizon　optimal　problems　of　discrete-time　nonlinear　stochastic　systems.　In　this　paper,　we　establish　a　data-driven　discounted　optimal　regulation　method　for　discrete-time　stochastic　systems　involving　adaptive　critic　technology.　First,　we　investigate　the　infinite-horizon　optimal　problems　with　the　discount　factor　for　stochastic　systems　under　the　relaxed　assumption.　The　developed　stochastic　Q-learning　algorithm　can　optimize　an　initial　admissible　policy　to　the　optimal　one　in　a　monotonically　nonincreasing　way.　Based　on　the　data-driven　idea,　the　policy　optimization　of　the　stochastic　Q-learning　algorithm　is　executed　without　a　dynamic　model.　Then,　the　stochastic　Q-learning　algorithm　is　implemented　by　utilizing　the　actor-critic　neural　networks.　Finally,　two　nonlinear　benchmarks　are　given　to　demonstrate　the　overall　performance　of　the　developed　stochastic　Q-learning　algorithm.　©　2024　Science　Press.　All　rights　reserved.