Accelerated Regularized Wasserstein Proximal Sampling Algorithms
This work addresses sampling efficiency for probabilistic models, particularly in non-log-concave settings like Bayesian neural networks, but it appears incremental as it builds on existing proximal and acceleration techniques.
The paper tackles sampling from Gibbs distributions by introducing an accelerated regularized Wasserstein proximal method (ARWP) that uses a second-order score-based ODE for faster particle evolution, resulting in higher contraction rates and improved mixing compared to existing methods like kinetic Langevin.
We consider sampling from a Gibbs distribution by evolving a finite number of particles using a particular score estimator rather than Brownian motion. To accelerate the particles, we consider a second-order score-based ODE, similar to Nesterov acceleration. In contrast to traditional kernel density score estimation, we use the recently proposed regularized Wasserstein proximal method, yielding the Accelerated Regularized Wasserstein Proximal method (ARWP). We provide a detailed analysis of continuous- and discrete-time non-asymptotic and asymptotic mixing rates for Gaussian initial and target distributions, using techniques from Euclidean acceleration and accelerated information gradients. Compared with the kinetic Langevin sampling algorithm, the proposed algorithm exhibits a higher contraction rate in the asymptotic time regime. Numerical experiments are conducted across various low-dimensional experiments, including multi-modal Gaussian mixtures and ill-conditioned Rosenbrock distributions. ARWP exhibits structured and convergent particles, accelerated discrete-time mixing, and faster tail exploration than the non-accelerated regularized Wasserstein proximal method and kinetic Langevin methods. Additionally, ARWP particles exhibit better generalization properties for some non-log-concave Bayesian neural network tasks.