Minimizing the Profligacy of Searches with Reset
arxiv(2024)
Abstract
We introduce the profligacy of a search process as a competition between its
expected cost and the probability of finding the target. The arbiter of the
competition is a parameter λ that represents how much a searcher
invests into increasing the chance of success. Minimizing the profligacy with
respect to the search strategy specifies the optimal search. We show that in
the case of diffusion with stochastic resetting, the amount of resetting in the
optimal strategy has a highly nontrivial dependence on model parameters
resulting in classical continuous transitions, discontinuous transitions and
tricritical points as well as non-standard discontinuous transitions exhibiting
re-entrant behavior and overhangs.
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