In　this　paper,　we　study　approximation　algorithms　for　several　classes　of　DR-submodular　optimization　problems,　where　DR　is　short　for　diminishing　return.　Following　a　newly　introduced　algorithm　framework　for　zeroth-order　stochastic　approximation　methods,　we　first　propose　algorithms　CG-ZOSA　and　RG-ZOSA　for　smooth　DR-submodular　optimization　based　on　the　coordinate-wise　gradient　estimator　and　the　randomized　gradient　estimator,　respectively.　Our　theoretical　analysis　proves　that　CG-ZOSA　can　reach　a　solution　whose　expected　objective　value　exceeds　(1　e(-1)　-is　an　element　of(2))OPT　-is　an　element　of　after　O(-is　an　element　of(-2)　)　iterations　and　O(N-2/3　d　is　an　element　of(-2))　oracle　calls,　where　d　represents　the　problem　dimension.　On　the　other　hand,　RG-ZOSA　improves　the　approximation　ratio　to　(1-e(-1)-is　an　element　of(2)/d)　while　maintaining　the　same　overall　oracle　complexity.　For　non-smooth　up-concave　maximization　problems,　we　propose　a　novel　auxiliary　function　based　on　a　smoothed　objective　function　and　introduce　the　NZOSA　algorithm.　This　algorithm　achieves　an　approximation　ratio　of　(1-e(-1　)-is　an　element　of　ln　is　an　element　of(-1)-is　an　element　of(2)ln　is　an　element　of(-1))　with　O(d　is　an　element　of(-2))　iterations　and　O　(N-2/3　d(3/2)　is　an　element　of(-3))　oracle　calls.　We　also　extend　NZOSA　to　handle　a　class　of　robust　DR-submodular　maximization　problems.　To　validate　the　effectiveness　of　our　proposed　algorithms,　we　conduct　experiments　on　both　synthetic　and　real-world　problems.　The　results　demonstrate　the　superior　performance　and　efficiency　of　our　methods　in　solving　DR-submodular　optimization　problems.