  We present a method to probe rare molecular dynamics trajectories directly
using reinforcement learning. We consider trajectories that are conditioned to
transition between regions of configuration space in finite time, like those
relevant in the study of reactive events, as well as trajectories exhibiting
rare fluctuations of time-integrated quantities in the long time limit, like
those relevant in the calculation of large deviation functions. In both cases,
reinforcement learning techniques are used to optimize an added force that
minimizes the Kullback-Leibler divergence between the conditioned trajectory
ensemble and a driven one. Under the optimized added force, the system evolves
the rare fluctuation as a typical one, affording a variational estimate of its
likelihood in the original trajectory ensemble. Low variance gradients
employing value functions are proposed to increase the convergence of the
optimal force. The method we develop employing these gradients leads to
efficient and accurate estimates of both the optimal force and the likelihood
of the rare event for a variety of model systems.
