Finite horizon exploration for path integral control problems

We have recently developed a path integral method for solving a class of non-linear stochastic control problems in the continuous domain [1, 2]. Path integral (PI) control can be applied for timedependent finite-horizon tasks (motor control, coordination between agents) and static tasks (which behave similar to discounted reward reinforcement learning). In this control formalism, the cost-togo or value function can be solved explicitly as a function of the environment and rewards (as a path integral). Thus, for PI control one does not need to solve the Bellman equation. The computation of the path integral can also be complex, but one can use methods and concepts from statistical physics, such as Monte Carlo sampling or the Laplace approximation to obtain efficient approximations.