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 $\varepsilon$ error in chi-square divergence with a computational cost equivalent to $O\bigl(\kappa^2 d^\frac{1}{2}(\log\frac{1}{\varepsilon})^{\frac{3}{2}}\bigr)$ gradient evaluations in the regime $\kappa \ll \frac{d}{\log d}$ under a warm start assumption, where $\kappa$ is the condition number and $d$ is the dimension.
翻译：我们研究Zigzag 抽样算法的计算复杂性。 zigzag 过程的优点是不需要时间分解执行, 并且每个拟议的弹簧事件只需要对潜力的部分衍生物进行一次评价, 而其趋同率是独立的。 我们使用这些属性, 我们证明 zigzag 取样算法在热启动假设下, 千平方元在千平方元中实现了$\varepsilon 的错误, 而计算成本相当于$O\bigl(\kappa2 d ⁇ frac{1 ⁇ 2} (\log\frac{1\unvarepsilon}) {\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
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