Mean-performance of sharp restart I: Statistical roadmap

Abstract

Restart is a general framework, of prime importance and wide applicability, for expediting first-passage times and completion times of general stochastic processes. Restart protocols can use either deterministic or stochastic timers. Restart protocols with deterministic timers -- "sharp restart" -- assume a principal role: if there exists a restart protocol that improves mean-performance, then there exists a sharp-restart protocol that performs as good or better. This paper, the first of a duo, presents a comprehensive mean-performance analysis of sharp restart. Using statistical methods, the analysis establishes universal criteria that determine when sharp restart improves or worsens mean-performance, i.e., decreases or increases mean first-passage/completion times. These criteria are akin to those recently discovered for the most widely applied restart protocols -- "exponential restart" -- which use exponentially-distributed timers. However, while the exponential-restart criteria cover only the case of slow timers, the sharp-restart criteria established here further cover the cases of fast, critical, and general timers; moreover, the latter criteria address the very existence of timers with which sharp restart improves or worsens mean-performance. Using the slow-timers criteria, we discover a general scenario for which: sharp restart improves mean-performance, whereas exponential restart worsens mean-performance. The potency of the novel results presented here is demonstrated by examples, and by the results' application to canonical diffusion processes.

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Cited by in corpus (21)

• The inspection paradox in stochastic resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Diffusion with Partial Resetting
• Diffusion with Local Resetting and Exclusion
• Mitigating long queues and waiting times with service resetting
• Discrete space-time resetting model: Application to first-passage and transmission statistics
• A Unified Approach to Gated Reactions on Networks
• Diffusion with two resetting points
• Mean-performance of Sharp Restart II: Inequality Roadmap
• Tail-behavior roadmap for sharp restart
• Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?
• Capture of a diffusing lamb by a diffusing lion when both return home
• Diversity of Sharp Restart
• Stochastic resetting prevails over sharp restart for broad target distributions
• Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables
• Entropy of Sharp Restart
• Continuous Gated First-Passage Processes
• First-Passage Approach to Optimizing Perturbations for Improved Training of Machine Learning Models
• The distribution of the maximum of independent resetting Brownian motions
• Arcsine laws for Brownian motion with Poissonian resetting
• Chaotic resetting: A resetting strategy for deterministic chaotic systems