# Restart could optimize the probability of success in a Bernoulli trial

## TL;DR

This paper explores how restart strategies can optimize the likelihood of achieving a desired outcome in Bernoulli-like stochastic processes, revealing universal principles for maximizing success probability.

## Contribution

It demonstrates that restart can significantly influence splitting probabilities in Bernoulli processes and identifies conditions for optimal restart to maximize success likelihood.

## Key findings

- Restart can alter the probability of process outcomes.
- Optimal restart strategies can maximize the chance of desired completion.
- Universal aspects of optimal restart behavior are identified.

## 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.