Utilizing Priors in Sampling-based Cost Minimization

We consider an autonomous vehicle (AV) agent performing a long-term cost-minimization problem in the elapsed time $T$ over sequences of states $s_{1:T}$ and actions $a_{1:T}$ for some fixed, known (though potentially learned) cost function $C(s_t,a_t)$, approximate system dynamics $P$, and distribution over initial states $d_0$. The goal is to minimize the expected cost-to-go of the driving trajectory $\tau =s_1,a_1,\mathrm{.}\mathrm{.}\mathrm{.},s_T,a_T$ from the initial state.