Restarting is a technique frequently employed in randomized algorithms. After some number of computation steps, the state of the algorithm is reinitialized with a new, independent random seed. Luby et al. (Inf. Process. Lett. 47(4), 173–180, 1993) introduced a universal restart strategy. They showed that their strategy is an optimal universal strategy in the worst case. However, the optimality result has only been shown for discrete processes. In this work, it is shown that their result does not translate into a continuous setting. Furthermore, we show that there are no (asymptotically) optimal strategies in a continuous setting. Nevertheless, we obtain an optimal universal strategy on a restricted class of continuous probability distributions. Furthermore, as a side result, we show that the expected value under restarts for the lognormal distribution tends towards 0. Finally, the results are illustrated using simulations.

重新启动是随机算法中经常采用的一种技术。经过一定数量的计算步骤后，将使用新的独立随机种子重新初始化算法的状态。卢比（Luby）等人。（INF组成。过程快报。47（4），173–180，1993）引入了通用重启策略。他们表明，在最坏的情况下，他们的策略是最佳的通用策略。但是，仅针对离散过程显示了最佳结果。在这项工作中，表明他们的结果不会转换为连续的设置。此外，我们证明了在连续设置中没有（渐近）最优策略。然而，我们在连续概率分布的受限类中获得了最优的通用策略。此外，作为副结果，我们显示了在重新启动下对数正态分布的期望值趋于0。最后，使用模拟对结果进行了说明。