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DeePC-Hunt: Data-enabled Predictive Control Hyperparameter Tuning via Differentiable Optimization

Michael Cummins, Alberto Padoan, Keith Moffat, Florian Dorfler, John Lygeros

TL;DR

DeePC-Hunt addresses the challenge of tuning DeePC hyperparameters by framing them as differentiable components within a closed-loop optimization. By backpropagating through the DeePC policy with an approximate surrogate model, it optimizes the regularization vector $\boldsymbol{\lambda}$ using a projected resilient backpropagation scheme and differentiable optimization layers. The approach is validated on a nonlinear VTVL landing task, where DeePC-Hunt demonstrates superior robustness to model misspecification compared with a baseline MPC approach, and achieves competitive or better closed-loop performance with offline hyperparameter tuning. The work highlights a practical path to automate parameter tuning in data-driven predictive control, reducing sim-to-real gaps and enabling safer, more reliable deployments. The methodology leverages Hankel data representations, CVXPYLayers, and Monte Carlo gradient estimation to enable efficient offline optimization of hyperparameters for complex, nonlinear systems.

Abstract

This paper introduces Data-enabled Predictive Control Hyperparameter Tuning via Differentiable Optimization (DeePC-Hunt), a backpropagation-based method for automatic hyperparameter tuning of the DeePC algorithm. The necessity for such a method arises from the importance of hyperparameter selection to achieve satisfactory closed-loop DeePC performance. The standard methods for hyperparameter selection are to either optimize the open-loop performance, or use manual guess-and-check. Optimizing the open-loop performance can result in unacceptable closed-loop behavior, while manual guess-and-check can pose safety challenges. DeePC-Hunt provides an alternative method for hyperparameter tuning which uses an approximate model of the system dynamics and backpropagation to directly optimize hyperparameters for the closed-loop DeePC performance. Numerical simulations demonstrate the effectiveness of DeePC in combination with DeePC-Hunt in a complex stabilization task for a nonlinear system and its superiority over model-based control strategies in terms of robustness to model misspecifications.

DeePC-Hunt: Data-enabled Predictive Control Hyperparameter Tuning via Differentiable Optimization

TL;DR

DeePC-Hunt addresses the challenge of tuning DeePC hyperparameters by framing them as differentiable components within a closed-loop optimization. By backpropagating through the DeePC policy with an approximate surrogate model, it optimizes the regularization vector using a projected resilient backpropagation scheme and differentiable optimization layers. The approach is validated on a nonlinear VTVL landing task, where DeePC-Hunt demonstrates superior robustness to model misspecification compared with a baseline MPC approach, and achieves competitive or better closed-loop performance with offline hyperparameter tuning. The work highlights a practical path to automate parameter tuning in data-driven predictive control, reducing sim-to-real gaps and enabling safer, more reliable deployments. The methodology leverages Hankel data representations, CVXPYLayers, and Monte Carlo gradient estimation to enable efficient offline optimization of hyperparameters for complex, nonlinear systems.

Abstract

This paper introduces Data-enabled Predictive Control Hyperparameter Tuning via Differentiable Optimization (DeePC-Hunt), a backpropagation-based method for automatic hyperparameter tuning of the DeePC algorithm. The necessity for such a method arises from the importance of hyperparameter selection to achieve satisfactory closed-loop DeePC performance. The standard methods for hyperparameter selection are to either optimize the open-loop performance, or use manual guess-and-check. Optimizing the open-loop performance can result in unacceptable closed-loop behavior, while manual guess-and-check can pose safety challenges. DeePC-Hunt provides an alternative method for hyperparameter tuning which uses an approximate model of the system dynamics and backpropagation to directly optimize hyperparameters for the closed-loop DeePC performance. Numerical simulations demonstrate the effectiveness of DeePC in combination with DeePC-Hunt in a complex stabilization task for a nonlinear system and its superiority over model-based control strategies in terms of robustness to model misspecifications.

Paper Structure

This paper contains 12 sections, 17 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Differentiable Convex Optimization Layers
  4. The DeePC Algorithm
  5. Projected Resilient Backpropagation
  6. DeePC-Hunt
  7. Numerical Simulation: landing a VTVL vehicle
  8. Rocket Lander Gym Environment
  9. MPC Policy
  10. DeePC-Hunt Policy
  11. Evaluation of Control Performance
  12. Conclusion

Figures (3)

  • Figure 1: The DeePC policy is instantiated using CvxpyLayers and PyTorch to enable automatic differentiation. Simulations are carried out on an approximate model of the system and projected resilient backpropagation is used to update the hyperparameters.
  • Figure 2: Free body diagram of the VTVL rocket from Ferrante2017ARC.
  • Figure 3: Performance of the MPC (top) and DeePC-Hunt (bottom) policies using models A (left) and B (right), respectively.