We consider an unconstrained problem of minimizing a smooth convex function
which is only available through noisy observations of its values, the noise
consisting of two parts. Similar to stochastic optimization problems, the first
part is of stochastic nature. The second part is additive noise of unknown
nature, but bounded in absolute value. In the two-poi
本文探讨了在带有巴氏反馈或者没有梯度知识下的凸随机优化问题。我们通过精确表征强凸平滑函数的性能以及非凸平滑函数的性能下界，证明了在这两种情况下，所需的查询次数至少要实现二次比例尺度关系。我们同时还发现对于二次函数，即使在没有梯度信息的情况下，也可以在平方次的询问内实现 O (1/T) 的误差率。此结果是在派生式随机情况下的首次结果，并且在之前暗示相反的情况下，依然成立。