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Global Optimization via Schr{\'o}dinger-F{\'o}llmer Diffusion
- Publication Year :
- 2021
-
Abstract
- We study the problem of finding global minimizers of $V(x):\mathbb{R}^d\rightarrow\mathbb{R}$ approximately via sampling from a probability distribution $\mu_{\sigma}$ with density $p_{\sigma}(x)=\dfrac{\exp(-V(x)/\sigma)}{\int_{\mathbb R^d} \exp(-V(y)/\sigma) dy }$ with respect to the Lebesgue measure for $\sigma \in (0,1]$ small enough. We analyze a sampler based on the Euler-Maruyama discretization of the Schr{\"o}dinger-F{\"o}llmer 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 $\mathcal{O}(d^{3})$ standard normal random variables. Numerical studies illustrate the effectiveness of the proposed method and its superiority to the Langevin method.<br />Comment: arXiv admin note: text overlap with arXiv:2107.04766
- Subjects :
- Mathematics - Optimization and Control
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2111.00402
- Document Type :
- Working Paper