In　this　paper,　we　study　the　problem　of　maximizing　a　nonmonotone　one-sided-　η　smooth　(OSS　for　short)　function　ψ(x)　under　a　downwards-closed　convex　polytope　constraint.　The　concept　of　OSS　was　first　proposed　by　Mehrdad　et　al.　[1,　2]　to　express　the　properties　of　multilinear　extension　of　some　set　functions.　It　is　a　generalization　of　the　continuous　DR　submodular　function.　The　OSS　property　guarantees　an　alternative　bound　based　on　Taylor　expansion.　If　the　objective　function　is　nonmonotone　diminishing　return　(DR)　submodular,　Bian　et　al.　[3]　gave　a　1/e　approximation　algorithm　with　a　regret　bound　O(LD22K).　On　general　convex　sets,　D　ü　rr　et　al.　[4]　gave　a　133　approximation　solution　with　O(LD2(lnK)2)　regrets.　In　this　paper,　we　consider　maximizing　the　more　general　OSS　function,　and　by　adjusting　the　iterative　step　of　the　Jump-Start　Frank　Wolfe　algorithm,　an　approximation　of　1/e　can　still　be　obtained　in　the　case　of　a　larger　regret　bound　O(L(μD)22K).　(where　L,　μ,　D　are　some　parameters,　see　Table 1).　The　larger　the　parameter　η　we　choose,　the　more　regrets　we　will　receive,　because　of　μ=(ββ+1)-2η　(β∈　(0,　1　]　).　©　2023,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG.