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arXiv · 2102.13154

Mean-performance of Sharp Restart II: Inequality Roadmap

Iddo Eliazar·Shlomi Reuveni
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Abstract

Restarting a deterministic process always impedes its completion. However, it is known that restarting a random process can also lead to an opposite outcome -- expediting completion. Hence, the effect of restart is contingent on the underlying statistical heterogeneity of the process' completion times. To quantify this heterogeneity we bring a novel approach to restart: the methodology of inequality indices, which is widely applied in economics and in the social sciences to measure income and wealth disparity. Using this approach we establish an `inequality roadmap' for the mean-performance of sharp restart: a whole new set of universal inequality criteria that determine when restart with sharp timers (i.e. with fixed deterministic timers) decreases/increases mean completion. The criteria are based on a host of inequality indices including Bonferroni, Gini, Pietra, and other Lorenz-curve indices; each index captures a different angle of the restart-inequality interplay. Utilizing the fact that sharp restart can match the mean-performance of any general restart protocol, we prove -- with unprecedented precision and resolution -- the validity of the following statement: restart impedes/expedites mean completion when the underlying statistical heterogeneity is low/high.

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BibTeXRIS

Iddo Eliazar, Shlomi Reuveni. 2021-02-25. Mean-performance of Sharp Restart II: Inequality Roadmap. https://doi.org/10.1088/1751-8121%2Fac16c5

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