Optimizing cost through dynamic stochastic resetting

Abstract

The cost of stochastic resetting is considered within the context of a discrete random walk (RW) model. In addition to standard stochastic resetting, for which a reset occurs with a certain probability after each step, we introduce a novel resetting protocol which we dubbed dynamic resetting. This protocol entails an additional dynamic constraint related to the direction of successive steps of the RW. We study this novel protocol for a one-dimensional RW 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.