随机 最优化 Applications of such bandit problems include online auctions and advertisement selection for search engines. Similarly, the field of simulation-based optimization provides many examples of problems in which optimization is performed based only on function values [27] [11] [25]. Finally, in many problems in statistics—includi ng graphical model inference problems [30] and structured-prediction problems [28]—the objective is defined variationally (as the maximum of a family of functions), so explicit differentiation may be difficult. ng graphical model inference problems [30] and structured-prediction problems [28]—the objective is defined variationally (as the maximum of a family of functions), so explicit differentiation may be difficult.