Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networks

TL;DR

This paper introduces a supervised learning framework for explicit model predictive control that includes a certificate policy to estimate sub-optimality online, enabling fast and reliable control on resource-limited systems.

Contribution

It presents a novel approach to learn control and certificate policies simultaneously, providing probabilistic guarantees on feasibility and optimality without requiring real-time optimization.

Findings

Achieved up to 100x speedup in control computation.

Provided probabilistic bounds on policy infeasibility and suboptimality.

Demonstrated effectiveness on vehicle dynamics control.

Abstract

In this paper, we propose a novel framework for approximating the explicit MPC law for linear parameter-varying systems using supervised learning. In contrast to most existing approaches, we not only learn the control policy, but also a "certificate policy", that allows us to estimate the sub-optimality of the learned control policy online, during execution-time. We learn both these policies from data using supervised learning techniques, and also provide a randomized method that allows us to guarantee the quality of each learned policy, measured in terms of feasibility and optimality. This in turn allows us to bound the probability of the learned control policy of being infeasible or suboptimal, where the check is performed by the certificate policy. Since our algorithm does not require the solution of an optimization problem during run-time, it can be deployed even on resource-constrained systems. We illustrate the efficacy of the proposed framework on a vehicle dynamics control problem where we demonstrate a speedup of up to two orders of magnitude compared to online optimization with minimal performance degradation.