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In this paper, we propose a novel uniform generalization bound on the timeand inverse temperature for stochastic gradient Langevin dynamics (SGLD) in anon-convex setting. While previous works derive their generalization bounds byuniform stability, we use Rademacher complexity to make our generalizationbound independent of the time and inverse temperature. Using Rademachercomplexity, we can reduce the problem to derive a generalization bound on thewhole space to that on a bounded region and therefore can remove the effect ofthe time and inverse temperature from our generalization bound. As anapplication of our generalization bound, an evaluation on the effectiveness ofthe simulated annealing in a non-convex setting is also described. For thesample size $n$ and time $s$, we derive evaluations with orders $\sqrt{n^{-1}\log (n+1)}$ and $|(\log)^4(s)|^{-1}$, respectively. Here, $(\log)^4$ denotesthe $4$ times composition of the logarithmic function.

Uniform Generalization Bound on Time and Inverse Temperature for Gradient Descent Algorithm and its Application to Analysis of Simulated Annealing