Adaptive resetting for informed search strategies and the design of non-equilibrium steady-states

Stochastic resetting, the procedure of stopping and re-initializing random processes, has recently emerged as a powerful tool for accelerating processes ranging from queuing systems to molecular simulations. However, its usefulness is severely limited by assuming that the resetting protocol is completely decoupled from the state and age of the process that is being reset. We present a general formulation for state- and time-dependent resetting of stochastic processes, which we call adaptive resetting. This allows us to predict, using a single set of trajectories without resetting and via a simple reweighing procedure, all key observables of processes with adaptive resetting. These include the first-passage time distribution, the propagator, and the steady-state. Our formulation enables efficient exploration of informed search strategies and facilitates the prediction and design of complex non-equilibrium steady-states, eliminating the need for extensive brute-force sampling across different resetting protocols. Finally, we develop a general machine learning framework to optimize the adaptive resetting protocol for an arbitrary task beyond the current state of the art. We use it to discover efficient protocols for accelerating molecular dynamics simulations.