Optimizing Cost through Dynamic Stochastic Resetting

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.
Comment: 21 pages, 15 figures