Combined　with　policy-based　reinforcement　learning　(RL)　and　value-based　RL,　the　actor-critic　(AC)　learning　structure　is　an　effective　framework.　However,　the　cost　function　of　this　AC　framework　has　large　variances,　which　make　it　difficult　to　accomplish　an　optimization　objective.　Based　on　the　discounted　generalized　value　iteration　method　with　ℓ1-regularization,　a　regularized　AC　(RAC)　framework　is　developed　to　address　the　optimal　regulation　problems　and　make　the　cost　function　converge　faster.　Two　neural　networks　are　constructed　to　update　the　cost　function　and　the　policy　gradient,　respectively.　The　ℓ1-regularization　is　used　in　the　policy　gradient　and　the　cost　function　in　the　process　of　value　iteration.　The　cost　function　is　proved　to　converge　to　the　optimal　cost　function　in　a　monotonically　decreasing　form.　Finally,　the　effectiveness　of　RAC　is　shown　through　two　experiments.　　©　2023　IEEE.