Chance-Constrained Neural MPC under Uncontrollable Agents via Sequential Convex Programming

This work investigates the challenge of ensuring safety guarantees in the presence of uncontrollable agents, whose behaviors are stochastic and depend on both their own and the system's states. We present a neural model predictive control (MPC) framework that predicts the trajectory of the uncontrollable agent using a predictor learned from offline data. To provide formal probabilistic guarantees on prediction errors despite policy-induced distribution shifts, we propose a region-wise robust conformal prediction scheme to construct time-dependent uncertainty bounds, which are integrated into the MPC formulation. To solve the resulting non-convex, discontinuous optimization problem, we propose a two-loop iterative sequential convex programming algorithm. The inner loop solves convexified subproblems with fixed error bounds, while the outer loop refines these bounds based on updated control sequences. We establish convergence guarantees and analyze the optimality of the algorithm. We illustrate our method with an autonomous driving scenario involving interactive pedestrians. Experimental results demonstrate that our approach achieves superior safety and efficiency compared to baseline methods, with success rates exceeding 99.5% while maintaining higher average speeds in multi-pedestrian scenarios.