Convergence Analysis of Schr{ö}dinger-F{ö}llmer Sampler without Convexity
Schr\"{o}dinger-F\"{o}llmer 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 Schr\"{o}dinger-F\"{o}llmer 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.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Bayesian Learning via Neural Schrödinger-Föllmer Flows
In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schr\"odinger bridges). We advocate stochastic control as a finite time and low variance alte…
Bayesian InferenceLocalized Schrödinger Bridge Sampler
We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. In this paper, we build on previous work combining Schr\"odinger bridges and …
Bayesian InferenceDenoisingDiscrete Adjoint Schrödinger Bridge Sampler
Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schrödinger bridge (SB) provide principled solutions, efficient SOC s…
Schrödinger Bridge Samplers
Consider a reference Markov process with initial distribution $\pi_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $\pi_{T}$, which is not equal to t…
Asymptotics of Discrete Schrödinger Bridges via Chaos Decomposition
Consider the problem of matching two independent i.i.d. samples of size $N$ from two distributions $P$ and $Q$ in $\mathbb{R}^d$. For an arbitrary continuous cost function, the optimal assignment problem looks for the ma…