The　online　optimization　model　was　first　introduced　in　the　research　of　machine　learning　problems　(Zinkevich,　Proceedings　of　ICML,　928-936,　2003).　It　is　a　powerful　framework　that　combines　the　principles　of　optimization　with　the　challenges　of　online　decision-making.　The　present　research　mainly　consider　the　case　that　the　reveal　objective　functions　are　convex　or　submodular.　In　this　paper,　we　focus　on　the　online　maximization　problem　under　a　special　objective　function　Phi(x)　:　[0,1](n)　-＞　R+　which　satisfies　the　inequality　1/2　＜　u(T)　del(2)Phi(x),　u　＞　＜=　sigma　center　dot　||u||(1)/||x||(1)　＜　u,　del　Phi(x)＞　for　any　x,　u　is　an　element　of[0,　1](n),　x　not　equal　0.　This　objective　function　is　named　as　one　sided　sigma-smooth　(OSS)　function.　We　achieve　two　conclusions　here.　Firstly,　under　the　assumption　that　the　gradient　function　of　OSS　function　is　L-smooth,　we　propose　an　(1-exp((theta　-　1)(theta/(1+theta))(2　sigma)))-　approximation　algorithm　with　O(root　T)　regret　upper　bound,　where　T　is　the　number　of　rounds　in　the　online　algorithm　and　theta,　sigma　is　an　element　of　R+　are　parameters.　Secondly,　if　the　gradient　function　of　OSS　function　has　no　L-smoothness,　we　provide　an　(1　+　((theta　+　1)/theta)(4　sigma))(-1)-approximation　projected　gradient　algorithm,　and　prove　that　the　regret　upper　bound　of　the　algorithm　is　O(root　T).　We　think　that　this　research　can　provide　different　ideas　for　online　non-convex　and　non-submodular　learning.