Diversity of sharp restart

Abstract

When applied to a stochastic process of interest, a restart protocol alters the overall statistical distribution of the process’ completion time; thus, the completion-time’s mean and randomness change. The explicit effect of restart on the mean is well understood, and it is known that: from a mean perspective, deterministic restart protocols – termed sharp restart – can out-perform any other restart protocol. However, little is known on the explicit effect of restart on randomness. This paper is the second in a duo exploring the effect of sharp restart on randomness: via a Boltzmann-Gibbs-Shannon entropy analysis in the first part, and via a diversity analysis in this part. Specifically, gauging randomness via diversity – a measure that is intimately related to the Renyi entropy – this paper establishes a set of universal criteria that determine: A) precisely when a sharp-restart protocol decreases/increases the diversity of completion times; B) the very existence of sharp-restart protocols that decrease/increase the diversity of completion times. Moreover, addressing jointly mean-behavior and random-ness, this paper asserts and demonstrates when sharp restart has an aligned effect on the two (decreasing/increasing both), and when the effect is antithetical (decreasing one while increasing the other). The joint mean-diversity results require remarkably little information regarding the (original) statistical distributions of completion times, and are remarkably practical and easy to implement.

Energy-based stochastic resetting can avoid noise-enhanced stability

“…We start applying resetting to our system at deterministic time intervals. This technique has also been called sharp restart [29]. We fix the resetting position to the given initial condition (x, y, ẋ, ẏ) = (0, 0, √ 2E 0 sin θ, √ 2E 0 cos θ ), where E 0 = 0.25.…”

Preface: stochastic resetting—theory and applications

“…Taking resetting times from the Gamma distribution, he investigates how mean first-passage times are affected by deviations from Poissonian resetting (exponential resetting times). Going beyond the mean, Eliazar and Reuveni analyze how resetting at constant time intervals (sharp resetting) affects the entropy and other diversity measures of the first passage time distribution [55,56].…”