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In this paper, we present the Bennett-type generalization bounds of thelearning process for i.i.d. samples, and then show that the generalizationbounds have a faster rate of convergence than the traditional results. Inparticular, we first develop two types of Bennett-type deviation inequality forthe i.i.d. learning process: one provides the generalization bounds based onthe uniform entropy number; the other leads to the bounds based on theRademacher complexity. We then adopt a new method to obtain the alternativeexpressions of the Bennett-type generalization bounds, which imply that thebounds have a faster rate o(N^{-1/2}) of convergence than the traditionalresults O(N^{-1/2}). Additionally, we find that the rate of the bounds willbecome faster in the large-deviation case, which refers to a situation wherethe empirical risk is far away from (at least not close to) the expected risk.Finally, we analyze the asymptotical convergence of the learning process andcompare our analysis with the existing results.

Bennett-type Generalization Bounds: Large-deviation Case and Faster Rate of Convergence