Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence

2023/05/24 by Riccardo Bonalli, Bonalli, Riccardo, Alessandro Rudi +1 · 1 citation
Computer Science · Decision Sciences · Physics and Astronomy · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2305.15557

openalex publication_date 2023/05/24 · openalex created_date 2023/05/28 · openalex updated_date 2026/08/01

Abstract

We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations, yielding theoretical estimates of non-asymptotic learning rates which, unlike previous works, become increasingly tighter when the regularity of the unknown drift and diffusion coefficients becomes higher. Our method being kernel-based, offline pre-processing may be profitably leveraged to enable efficient numerical implementation, offering excellent balance between precision and computational complexity.

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