Convergence Analysis of Schrödinger-Föllmer Sampler without Convexity

07/10/2021

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by   Yuling Jiao, et al.

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Schrödinger-Föllmer sampler (SFS) is a novel and efficient approach for sampling from possibly unnormalized distributions without ergodicity. SFS is based on the Euler-Maruyama discretization of Schrödinger-Föllmer diffusion process d X_t=-∇ U(X_t, t) d t+d B_t, t ∈[0,1], X_0=0 on the unit interval, which transports the degenerate distribution at time zero to the target distribution at time one. In <cit.>, the consistency of SFS is established under a restricted assumption that uniformly (on t) strongly a nonasymptotic error bound of SFS in Wasserstein distance under some smooth and bounded conditions on the density ratio of the target distribution over the standard normal distribution, but without requiring the strongly convexity of the potential.