ZipDrift: Generating Multimodal Short-Horizon MPC Costs with One-Step Drifting Models

Abstract

Short-horizon model predictive control (MPC) is fast but myopic. ZipMPC compensates by learning a context-dependent correction of the short-horizon cost that imitates a long-horizon expert. We observe that the optimal correction is often multimodal: when a slower opponent can be passed on either side, good corrections of opposite sign coexist, and the expert's choice between them hinges on tiny cost differences. Deterministic regression then averages modes or inherits inconsistent expert tie-breaking. We propose ZipDrift, which trains a one-step drifting generator over MPC cost corrections, tilted toward low closed-loop cost and learned only from cost evaluations of candidate corrections, without differentiating through the optimiser. A few generated candidates are ranked by a learned critic, and the model-based MPC then enforces dynamics and constraints. In a kinematic overtaking benchmark derived from ZipMPC, more than half of the contexts are bimodal and the manual short-horizon MPC crashes in 28% of them. With an eight-dimensional stagewise correction, evaluated on 1000 fresh contexts and five training seeds, ZipDrift with eight candidates crashes in 0.74% of episodes, compared with 3.4% for an idealised ZipMPC-style regressor and 2.1% for critic-ranked random candidates with the same budget. A mixture density network (MDN) with the same selection is equally good (0.76%). The benefit of drifting lies in sample quality: in a pre-specified test on further unseen contexts, a single drifting sample crashes in 8.7% of episodes against 13.2% for the MDN, and ZipDrift needs four candidates instead of eight to fall below 1%. With many candidates, all methods degrade as selection exploits errors of the critic.