New RSLMC sampling algorithms achieve uniform-in-time W2 error bounds of order O(sqrt(d) h) under gradient Lipschitz and log-Sobolev assumptions, with modified versions for superlinear gradient growth and supporting numerical examples.
By iteration, we employ1−u≤e −u, u >0to acquire E h ¯Yn+1 2pi ≤ 1− µh 2 n+1 E |x0|2p +M 3dph nX i=1 1− µh 2 i ≤e− µtn+1 2 E |x0|2p + 2M3dp µ
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When Langevin Monte Carlo Meets Randomization: New Sampling Algorithms with Non-asymptotic Error Bounds beyond Log-Concavity and Gradient Lipschitzness
New RSLMC sampling algorithms achieve uniform-in-time W2 error bounds of order O(sqrt(d) h) under gradient Lipschitz and log-Sobolev assumptions, with modified versions for superlinear gradient growth and supporting numerical examples.