Complexity of zigzag sampling algorithm for strongly log-concave distributions

Abstract

We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each proposed bouncing event requires only one evaluation of partial derivative of the potential, while its convergence rate is dimension independent. Using these properties, we prove that the zigzag sampling algorithm achieves ε error in chi-square divergence with a computational cost equivalent to O `κ2 d 1 2 plog 1 ε q 3 2 ˘gradient evaluations in the regime κ ! d log d under a warm start assumption, where κ is the condition number and d is the dimension.

Analysis of Langevin Monte Carlo from Poincaré to Log-Sobolev

“…total variation distance, 2-Wasserstein distance, or KL divergence), and is therefore more desirable. Of particular interest in this regard is the role of Rényi divergence guarantees for providing "warm starts" for high-accuracy samplers such as the Metropolis-adjusted Langevin algorithm [Che+21a; WSC21] and the zigzag sampler [LW20].…”