Abstract

Incorporating task-specific priors within a policy or network architecture is crucial for enhancing safety and improving representation and generalization in robotic control problems. Differentiable Model Predictive Control (MPC) layers have proven effective for embedding these priors, such as constraints and cost functions, directly within the architecture, enabling end-to-end training. However, current methods often treat the solver and the neural network as separate, independent entities, leading to suboptimal integration. In this work, we propose a novel approach that co-develops the solver and architecture unifying the optimization solver and network inference problems. Specifically, we formulate this as a joint fixed-point problem over the coupled network outputs and necessary conditions of the optimization problem. We solve this problem in an iterative manner where we alternate between network forward passes and optimization iterations. Through extensive ablations in various robotic control tasks, we demonstrate that our approach yields richer representations and more stable training, while naturally accommodating warm starts, a key requirement for MPC.

We present navigation experiment playbacks (from their respective hardware runs) using four different baselines. Obstacles turned red indicate collisions.

We demonstrate DEQ-MPC’s enhanced representation capabilities. First, DEQ-MPC variants scale more effectively with dataset size and model capacity. Second, they show less performance degradation as constraint complexity increases.