We present a PAC-Bayes-style generalization bound which enables the replacement of the KL-divergence with a variety of Integral Probability Metrics (IPM). We provide instances of this bound with the IPM being the total variation metric and the Wasserstein distance. A notable feature of the obtained bounds is that they naturally interpolate between classical uniform convergence bounds in the worst case (when the prior and posterior are far away from each other), and improved bounds in favorable cases (when the posterior and prior are close). This illustrates the possibility of reinforcing classical generalization bounds with algorithm- and data-dependent components, thus making them more suitable to analyze algorithms that use a large hypothesis space.

翻译：我们提出了一个PAC-Bayes式的概括化约束,能够用各种综合概率计量(IPM)取代KL-Diverence(IPM)。我们提供了与IPM(IPM)结合的实例,即全变异度和瓦塞尔斯坦距离。获得的界限的一个显著特征是,它们自然地在最坏的情况下(先变和后变之间相距遥远时)在古典统一趋同界限之间相互交错,在有利情况下(后变和先变接近时)改进界限。 这说明有可能用依赖算法和数据的组成部分加强古典的概括化界限,从而使它们更适合于分析使用大假设空间的算法。