2021/10/31 by Yin Dai, Dai, Yin, Yuling Jiao +7 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Statistical Methods and Inference #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2111.00402
openalex publication_date 2021/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of finding global minimizers of V(x):ℝd→ℝ approximately via sampling from a probability distribution μσ with density pσ(x)=\dfracexp(-V(x)/σ)∫\mathbb Rd exp(-V(y)/σ) dy with respect to the Lebesgue measure for σ∈ (0,1] small enough. We analyze a sampler based on the Euler-Maruyama discretization of the Schrödinger-Föllmer diffusion processes with stochastic approximation under appropriate assumptions on the step size s and the potential V. We prove that the output of the proposed sampler is an approximate global minimizer of V(x) with high probability at cost of sampling O(d3) standard normal random variables. Numerical studies illustrate the effectiveness of the proposed method and its superiority to the Langevin method.