A reinforcement learning approach to rare trajectory sampling

Abstract Very often when studying non-equilibrium systems one is interested in analysing dynamical behaviour that occurs with very low probability, so called rare events . In practice, since are by definition atypical, they difficult to access a statistically significant way. What required strategies ‘make typical’ can be generated on demand. Here we present such general approach adaptively construct dynamics efficiently samples atypical events. We do exploiting the methods of reinforcement learning (RL), which refers set machine techniques aimed at finding optimal maximise reward associated dynamics. consider perspective trajectory ensembles, whereby described terms ensemble reweighting. By minimising distance between reweighted and suitably parametrised controlled arrive similar those RL numerically approximate realises interest. As simple illustrations detail problem excursions random walker, for case finite time horizon; current statistics particle hopping ring geometry, an infinite horizon. discuss natural extensions ideas presented here, including continuous-time Markov systems, first passage problems non-Markovian