Optimizing Cost through Dynamic Stochastic Resetting

TL;DR

This paper introduces a novel dynamic resetting protocol for a one-dimensional random walk, analyzing its impact on search efficiency and cost, and proposing optimized strategies for minimizing resets and search time.

Contribution

It presents a new dynamic resetting protocol with directional constraints and analyzes its effects on mean-first passage time and reset costs in a random walk model.

Findings

Dynamic resetting affects mean-first passage time.

Cost of resets depends on target distance.

Optimized search strategies reduce total cost.

Abstract

The cost of stochastic resetting is considered within the context of a discrete random walk model. In addition to standard stochastic resetting, for which a reset occurs with a certain probability after \emph{each} step, we introduce a novel resetting protocol which we dubbed {\it dynamic resetting}. This protocol entails an additional dynamic constraint related to the direction of successive steps of the random walker. We study this novel protocol for a one-dimensional random walker on an infinite lattice. We analyze the impact of the constraint on the walker's mean-first passage time and the cost (fluctuations) of the resets as a function of distance of target from the resetting location. Further, cost optimized search strategies are discussed.