Restart could optimize the probability of success in a Bernoulli trial

Abstract

Recently noticed ability of restart to reduce the expected completion time of first-passage processes allows appealing opportunities for performance improvement in a variety of settings. However, complex stochastic processes often exhibit several possible scenarios of completion which are not equally desirable in terms of efficiency. Here we show that restart may have profound consequences on the splitting probabilities of a Bernoulli-like first-passage process, i.e. of a process which can end with one of two outcomes. Particularly intriguing in this respect is the class of problems where a carefully adjusted restart mechanism maximizes probability that the process will complete in a desired way. We reveal the universal aspects of this kind of optimal behaviour by applying the general approach recently proposed for the problem of first-passage under restart.

6 pages and 3 figures in the main text + 4 pages of supplementary information

References in corpus (17)

• First-passage times in complex scale-invariant media
• First Passage Under Restart
• First order transition for the optimal search time of Lévy flights with resetting
• Diffusion with resetting in arbitrary spatial dimension
• Probing microscopic origins of confined subdiffusion by first-passage observables
• Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions
• Mortality, Redundancy, and Diversity in Stochastic Search
• Hidden Complexity in the Isomerization Dynamics of Holliday Junctions
• Universal formula for the mean first passage time in planar domains
• The escape problem for mortal walkers
• Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes
• Optimal search strategies of space-time coupled random walkers with finite lifetimes
• Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows
• Diffusion-limited reactions and mortal random walkers in confined geometries
• Random walks and Brownian motion: A method of computation for first-passage times and related quantities in confined geometries
• Waiting Cycle Times and Generalized Haldane Equality in the Steady-state Cycle Kinetics of Single Enzymes
• Trapping and Escape in a Turbid Medium

Cited by in corpus (76)

• Stochastic Resetting and Applications
• Optimal mean first-passage time for a Brownian searcher subjected to resetting: experimental and theoretical results
• First passage under stochastic resetting in an interval
• Search with home returns provides advantage under high uncertainty
• The inspection paradox in stochastic resetting
• Work fluctuations and Jarzynski equality in stochastic resetting
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Landau theory of restart transitions
• Optimization in First-Passage Resetting
• First passage under restart with branching
• Stochastic resetting with stochastic returns using external trap
• Ising model with stochastic resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process
• On subdiffusive continuous time random walks with stochastic resetting
• Invariants of motion with stochastic resetting and space-time coupled returns
• Properties of additive functionals of Brownian motion with resetting
• Restart expedites quantum walk hitting times
• Stochastic resetting in interacting particle systems: A review
• Extremal statistics for stochastic resetting systems
• Local time of diffusion with stochastic resetting
• Stochastic processes subject to a reset-and-residence mechanism: transport properties and first arrival statistics
• Random acceleration process under stochastic resetting
• Diffusion with Resetting Inside a Circle
• Resetting with stochastic return through linear confining potential
• Diffusive transport on networks with stochastic resetting to multiple nodes
• First-passage Brownian functionals with stochastic resetting
• First passage in the presence of stochastic resetting and a potential barrier
• Anderson-like localization transition of random walks with resetting
• Mean-performance of sharp restart I: Statistical roadmap
• Comparison of two models of tethered motion
• Resetting transition is governed by an interplay between thermal and potential energy
• Diffusive search for a stochastically-gated target with resetting
• Synchronization in the Kuramoto model in presence of stochastic resetting
• Diffusion with Local Resetting and Exclusion
• Asymmetric Stochastic Resetting: Modeling Catastrophic Events
• Mitigating long transient time in deterministic systems by resetting
• First passage of a diffusing particle under stochastic resetting in bounded domains with spherical symmetry
• Robust random search with scale-free stochastic resetting
• Restart uncertainty relation for monitored quantum dynamics
• Optimization and Growth in First-Passage Resetting
• Asymptotic analysis of extended two-dimensional narrow capture problems
• Diffusion with two resetting points
• Instability in the quantum restart problem
• Median and Mode in First Passage under Restart
• Critical number of walkers for diffusive search processes with resetting
• Mean-performance of Sharp Restart II: Inequality Roadmap
• Expediting Feller process with stochastic resetting
• First-passage properties of mortal random walks: ballistic behavior, effective reduction of dimensionality, and scaling functions for hierarchical graphs
• Searching for clusters of targets under stochastic resetting
• Freezing transitions of Brownian particles in confining potentials
• Optimal Measurement Protocols in Quantum Zeno Effect
• Effects of mortality on stochastic search processes with resetting
• Biased random walk on random networks in presence of stochastic resetting: Exact results
• Measurement-induced resetting in open quantum systems
• Search with stochastic home-returns can expedite classical first passage under resetting
• Optimal conditions for first passage of jump processes with resetting
• Comparing the roles of time overhead and spatial dimensions on optimal resetting rate vanishing transitions, in Brownian processes with potential bias and stochastic resetting
• Efficiency of a microscopic heat engine subjected to stochastic resetting
• Target Search Optimization by Threshold Resetting
• Stochastic resetting prevails over sharp restart for broad target distributions
• Designing Autonomous Maxwell Demon via Stochastic Resetting
• Optimizing the random search of a finite-lived target by a Lévy flight
• Random resetting in search problems
• Universal performance bounds of restart
• Optimal mean first-passage time of a Brownian searcher with resetting in one and two dimensions: Experiments, theory and numerical tests
• Universal criterion for selective outcomes under stochastic resetting
• Conditioned backward and forward times of diffusion with stochastic resetting: a renewal theory approach
• Autocorrelation functions and ergodicity in diffusion with stochastic resetting
• Random Walks on Lattices. Influence of Competing Reaction Centers on Diffusion-Controlled Processes
• Local resetting with geometric confinement
• Stochastic 1D search-and-capture as a G/M/c queueing model
• First-Passage-Driven Boundary Recession
• Search of stochastically gated targets with diffusive particles under resetting
• The distribution of the maximum of independent resetting Brownian motions
• Transition in Splitting Probabilities of Quantum Walks