Which side to pass? ZipDrift generates multimodal MPC cost corrections in one step and finishes 600 test episodes collision-free
Synopsis
Short-horizon model predictive control runs fast but cannot see an opponent beyond its horizon, so it needs a learned, context-dependent cost correction; when passing is possible on either side, both corrections are good and deterministic regression averages them into the opponent. ZipDrift instead trains a one-step drifting generator over cost corrections, tilted by closed-loop cost and learned without differentiating through the optimiser, then generates a few candidates ranked by a learned critic. On a straight-track overtaking benchmark with an eight-dimensional stagewise correction, all 600 test episodes were collision-free, against a 4.0% crash rate for an idealised ZipMPC-style regressor.
Interpretation
The cost correction of a short-horizon model predictive controller is no longer collapsed to a single point but represented as a set of possible values, so left and right passing lines can coexist. ZipMPC and related weight-adaptation schemes learn a deterministic map from context to cost parameters, and regression training converges to the conditional mean of its labels. In an overtaking task built on the ZipMPC kinematic racing setup, 53.4% of contexts have a good-correction set split into two separated intervals, and the long-horizon expert has two local solutions in 91% of contexts, with their objective values differing by less than 0.5% in about half of those.
The training signal is only the closed-loop scalar cost of candidate corrections, with no gradient through the optimiser, so labels can come from the same hard-constraint solver used at deployment. ZipMPC relies on differentiable MPC to propagate imitation-loss gradients through the optimiser, which brings a local convex approximation, soft state constraints during training, and a mismatch between training and deployment solvers. Each training context required 65 closed-loop simulations, and labelling 800 contexts took 18 minutes on 28 CPU cores, with labelling embarrassingly parallel.
The generator proposes candidates close to labelled corrections, the critic only ranks among them, and the model-based MPC enforces dynamics and constraints. Ranking uniformly sampled candidates with the critic, or widening the search to 4096 uniform samples, does not substitute for generated proposals. With the eight-dimensional correction and the same budget of eight candidates, critic-ranked uniform samples crash in 2.0% (12/600) and ranking 4096 uniform samples in 3.2%, while ZipDrift with best-of selection crashed in none of the 600 test episodes.
Perspective
The conclusions rest on a deliberately minimal benchmark: a kinematic bicycle on a straight track, one opponent at constant speed, a correction chosen at decision time and held for the episode, and simulation only. The authors explicitly list full laps on curved tracks, the Pacejka model, more opponents and hardware experiments as not yet evaluated.
The authors note that ZipMPC recomputes the correction at every step, and a stochastic generator risks switching modes between steps; reusing the noise across steps or conditioning on the previously selected mode remains to be tested. The Gibbs characterisation and the best-of argument concern the choice of a correction, not closed-loop stability or recursive feasibility. With a one-dimensional correction, critic grid search or an MDN with the same budget performs as well as ZipDrift, and in eight dimensions the margin over the MDN is not statistically significant.