In　this　article,　we　construct　a　novel　generalized　policy　iteration　framework　to　address　optimal　regulation　problems　for　discrete-time　nonlinear　systems　in　a　more　efficient　way.　Relevant　properties　are　investigated　for　the　framework,　including　monotonicity　and　convergence　of　the　iterative　value　function　sequence　as　well　as　the　admissibility　of　the　iterative　control　policy.　Additionally,　an　innovative　approach　is　developed　to　seek　an　initial　admissible　control　policy　for　the　framework　with　an　adjustable　searching　speed.　Based　on　these,　an　evolving　control　algorithm　is　presented　with　stability　guarantee.　This　algorithm　employs　iterative　control　policies　for　system　control　during　the　computation　of　the　optimal　control　policy,　as　opposed　to　waiting　for　the　generation　of　the　optimal　control　policy　before　implementing　control.　Eventually,　two　simulation　experiments　are　conducted　with　real-world　physical　backgrounds,　in　order　to　illustrate　the　performance　of　the　proposed　strategy.