The Proximal Sampler has exponential convergence in relative Fisher information for strongly log-concave targets, matching the rate of continuous-time Langevin dynamics.
Jiaming Liang and Yongxin Chen
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Mixing Time of the Proximal Sampler in Relative Fisher Information via Strong Data Processing Inequality
The Proximal Sampler has exponential convergence in relative Fisher information for strongly log-concave targets, matching the rate of continuous-time Langevin dynamics.