论文标题
尖锐重启的熵
Entropy of Sharp Restart
论文作者
论文摘要
重新启动有可能加快或阻碍一般随机过程的完成时间。因此，均值绩效的问题是中心阶段：量化在利益过程中重新启动的应用如何影响其完成时间的平均值。超越平均值，重新启动如何影响完成时间的随机性度量知之甚少。本文是研究二重奏中第一个通过：通过以下方面解决此知识差距的第一本，量化了重新启动的全面分析（Keystone重新启动协议）会影响完成时间的Boltzmann-Gibbs-Shannon熵。该分析确立了用一般计时器，快速计时器（高频重置）和缓慢的计时器（低频重置）的急速重新启动的闭合结果。这些结果具有共同的结构：将完成时间的危险率与平坦基准测试 - 指数分布的恒定危险率，其熵等于完成时间的熵。此外，使用基于Kullback-Leibler距离的信息几何方法，分析确定了确定计时器的存在的结果，其应用的应用范围降低或增加了完成时间的熵。我们的工作首先阐明了重新启动与随机性之间的复杂相互作用 - 由Boltzmann-Gibbs-Shannon熵进行了测量。
Restart has the potential of expediting or impeding the completion times of general random processes. Consequently, the issue of mean-performance takes center stage: quantifying how the application of restart on a process of interest impacts its completion-time's mean. Going beyond the mean, little is known on how restart affects stochasticity measures of the completion time. This paper is the first in a duo of studies that address this knowledge gap via: a comprehensive analysis that quantifies how sharp restart -- a keystone restart protocol -- impacts the completion-time's Boltzmann-Gibbs-Shannon entropy. The analysis establishes closed-form results for sharp restart with general timers, with fast timers (high-frequency resetting), and with slow timers (low-frequency resetting). These results share a common structure: comparing the completion-time's hazard rate to a flat benchmark -- the constant hazard rate of an exponential distribution whose entropy is equal to the completion-time's entropy. In addition, using an information-geometric approach based on Kullback-Leibler distances, the analysis establishes results that determine the very existence of timers with which the application of sharp restart decreases or increases the completion-time's entropy. Our work sheds first light on the intricate interplay between restart and randomness -- as gauged by the Boltzmann-Gibbs-Shannon entropy.
