DEQ-MPC : Deep Equilibrium Model Predictive Control

Swaminathan Gurumurthy, Khai Nguyen, Arun L Bishop, J Zico Kolter, Zachary Manchester

Keywords: MPC, Model Predictive Control, Optimization, Differentiable Optimization, Control

TL;DR: Integrating differentiable MPC layers within NNets by posing it as a joint equilibrium finding problem over the network outputs and solver iterates, resulting in improved representation, gradients and warm-starting for robotic control tasks.

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 \textit{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 results in richer representations and more stable training, while naturally accommodating warm starting, a key requirement for MPC.

Submission Number: 918