无梯度 Lipschitz 连续性的动力学 Langevin MCMC 采样--强凸情况

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2024-06-11 DOI:10.1016/j.jco.2024.101873

Tim Johnston , Iosif Lytras , Sotirios Sabanis

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引用次数: 0

摘要

在这篇文章中，我们考虑了在汉密尔顿环境下从对数凹分布中采样的问题，而不假定目标梯度是全局 Lipschitz 的。我们提出了两种基于单调多边形（驯服）欧拉方案的算法，用于从目标度量中采样，并提供了每种算法的过程规律与目标度量之间的非渐近 2-Wasserstein 距离约束。最后，我们应用这些结果来约束相关优化问题的超额风险优化误差。

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Kinetic Langevin MCMC sampling without gradient Lipschitz continuity - the strongly convex case

In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algorithms based on monotone polygonal (tamed) Euler schemes, to sample from a target measure, and provide non-asymptotic 2-Wasserstein distance bounds between the law of the process of each algorithm and the target measure. Finally, we apply these results to bound the excess risk optimization error of the associated optimization problem.

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.