HMC and Langevin united in the unadjusted and convex case

02/02/2022

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by   Pierre Monmarché, et al.

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We consider a family of unadjusted HMC samplers, which includes standard position HMC samplers and discretizations of the underdamped Langevin process. A detailed analysis and optimization of the parameters is conducted in the Gaussian case. Then, a stochastic gradient version of the samplers is considered, for which dimension-free convergence rates are established for log-concave smooth targets, gathering in a unified framework previous results on both processes. Both results indicate that partial refreshments of the velocity are more efficient than standard full refreshments.