arXiv:2502.15006v2 Announce Type: replace-cross Abstract: A common problem when using model predictive control (MPC) in practice is the satisfaction of safety specifications beyond the prediction horizon. While theoretical works have shown that safety can be guaranteed by enforcing a suitable terminal set constraint or a sufficiently long prediction horizon, these techniques are difficult to apply and thus are rarely used by practitioners, especially in the case of general nonlinear dynamics. To solve this problem, we impose a tradeoff between exact recursive feasibility, computational tractability, and applicability to ``black-box'' dynamics by learning an approximate discrete-time control barrier function and incorporating it into a variational inference MPC (VIMPC), a sampling-based MPC paradigm. To handle the resulting state constraints, we further propose a new sampling strategy that greatly reduces the variance of the estimated optimal control, improving the sample efficiency, and enabling real-time planning on a CPU. The resulting Neural Shield-VIMPC (NS-VIMPC) controller yields substantial safety improvements compared to existing sampling-based MPC controllers, even under badly designed cost functions. We validate our approach in both simulation and real-world hardware experiments. Project website: https://mit-realm.github.io/ns-vimpc/.