Abstract: Firstly，the concepts of annealed entropy，growth function and VC dimension are proposed and the bounds on the rate of uniform convergence of learning process based on VC dimension are constructed.Secondly，on the basis of these bounds，the idea of the structural risk minimization principle based on birandom samples is presented.Finally，the consistency of this principle is proven and the bound on the asymptotic rate of convergence is derived.

摘要： 提出退火熵、生长函数和VC 维等概念，构建基于VC 维的学习过程一致收敛速度的界。以这些界为基础，给出基于双重随机样本的结构风险最小化原则。最后证明该原则是一致的并且推导出了关于渐近收敛速度的界。