A bound uniform over various loss-classes is given for data generated by stationary and phi-mixing processes, where the mixing time (the time needed to obtain approximate independence) enters the sample complexity only in an additive way. For slowly mixing processes this can be a considerable advantage over results with multiplicative dependence on the mixing time. The admissible loss-classes include functions with prescribed Lipschitz norms or smoothness parameters. The bound can also be applied to be uniform over unconstrained loss-classes, where it depends on local Lipschitz properties of the function on the sample path.

翻译：针对平稳和phi混合过程生成的数据，给出了一个在各类损失函数类上一致成立的界限，其中混合时间（获得近似独立性所需的时间）仅以加法形式影响样本复杂度。对于缓慢混合过程而言，这相较于混合时间呈乘法依赖关系的结果具有显著优势。所允许的损失函数类包括具有给定Lipschitz范数或光滑性参数的函数。该界限也可应用于无约束损失函数类，此时其依赖于样本路径上函数的局部Lipschitz性质。