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Learning What Matters: Task Tailored Dynamics Models through Differentiable MPC

Jan Węgrzynowski, Piotr Kicki, Grzegorz Czechmanowski, Krzysztof, Tadeusz Walas

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Key figure (auto-extracted from paper)

Weighting dynamics model prediction errors by their closed-loop task impact via differentiable MPC significantly improves robotic tracking performance without increasing model capacity.

Differentiable MPC Task-aware training Dynamics modeling Model Predictive Control Robotics Loss weighting

Problem

Traditional dynamics models for MPC are trained with uniform loss functions like MSE, which misallocates limited model capacity by treating all state prediction errors as equally important for closed-loop control.

Approach

The authors use differentiable MPC to analytically compute how each predicted state error affects the final task cost, then use these sensitivities to dynamically weight the training loss so the model prioritizes learning critical states.

Key results

Sensitivity-weighted loss reduces closed-loop tracking cost compared to uniform MSE and variance-based baselines
Performance gains scale with multi-step rollout length, achieving a 91.7% normalized cost reduction at p=4
Local, sample-dependent sensitivity weighting proves essential, as averaging sensitivities causes significant performance drops
Demonstrated applicability to high-speed autonomous racing tasks with highly contextual state importance

Why it matters

It enables more efficient and accurate model-based control for robotics by ensuring limited model capacity is allocated to states that actually matter for task success.

Abstract

In model-based control, dynamics models are typ- ically trained by minimizing open-loop prediction errors uni- formly across all states. However, due to finite model capacity, this misallocates representational power, as not all prediction errors impact the downstream closed-loop performance equally. In this extended abstract, we propose a task-aware training methodology for a prediction model used in the context of Model Predictive Control (MPC). By extracting analytical sensitivities via differentiable MPC, we construct a loss function that weights multi-step dynamics model prediction errors based on their impact on the closed-loop task cost. Experimental results on a simulated 7DoF manipulator demonstrate that our sensitivity-weighted loss significantly improves closed-loop tracking performance compared to standard Mean Squared Error (MSE) or variance-based state standardization.

Index terms

Optimization and Optimal Control Machine Learning for Robot Control Calibration and Identification