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arXiv · 2107.04766

Convergence Analysis of Schr{ö}dinger-F{ö}llmer Sampler without Convexity

Yuling Jiao·Lican Kang·Yanyan Liu·Youzhou Zhou
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Abstract

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 $$\mathrm{d} X_{t}=-\nabla U\left(X_t, t\right) \mathrm{d} t+\mathrm{d} B_{t}, \quad t \in[0,1],\quad X_0=0$$ on the unit interval, which transports the degenerate distribution at time zero to the target distribution at time one. In \cite{sfs21}, the consistency of SFS is established under a restricted assumption that %the drift term $b(x,t)$ the potential $U(x,t)$ is uniformly (on $t$) strongly %concave convex (on $x$). In this paper we provide 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.

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Yuling Jiao, Lican Kang, Yanyan Liu, Youzhou Zhou. 2021-07-10. Convergence Analysis of Schr{ö}dinger-F{ö}llmer Sampler without Convexity. https://arxiv.org/abs/2107.04766

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