Differentiable MPC for End-to-end Planning and Control (1810.13400v3)

Abstract: We present foundations for using Model Predictive Control (MPC) as a differentiable policy class for reinforcement learning in continuous state and action spaces. This provides one way of leveraging and combining the advantages of model-free and model-based approaches. Specifically, we differentiate through MPC by using the KKT conditions of the convex approximation at a fixed point of the controller. Using this strategy, we are able to learn the cost and dynamics of a controller via end-to-end learning. Our experiments focus on imitation learning in the pendulum and cartpole domains, where we learn the cost and dynamics terms of an MPC policy class. We show that our MPC policies are significantly more data-efficient than a generic neural network and that our method is superior to traditional system identification in a setting where the expert is unrealizable.

• The paper introduces a method to differentiate through non-convex MPC policies using a backward-pass modified iLQR solver, bridging model-based and RL approaches.
• The paper demonstrates superior data efficiency in imitation learning experiments on pendulum and cart-pole tasks compared to traditional neural network policies.
• The paper shows that optimizing task-specific imitation loss can outperform standard system identification when expert dynamics are unrealizable, ensuring robust control.

Overview of Differentiable Model Predictive Control (MPC) for End-to-End Planning and Control

The paper discusses the integration of Model Predictive Control (MPC) into reinforcement learning (RL) frameworks by formulating a differentiable class of policies. This approach aims to leverage the advantages of both model-free and model-based reinforcement learning techniques, particularly focusing on enhanced data efficiency and model interpretability.

Key Contributions

The paper introduces a novel method to differentiate through MPC policies by leveraging the Karush-Kuhn-Tucker (KKT) conditions of a convex approximation at the fixed point of the controller. The methodology facilitates the learning of cost and dynamics models in an end-to-end manner, effectively bridging the gap between learning dynamics/task-specific costs and robust decision-making processes in RL.

Significant Contributions:

1. Efficient Differentiation Through Non-Convex Optimization: The paper presents a strategy for differentiating through an iterative, non-convex optimization procedure by employing a box-constrained iterative Linear Quadratic Regulator (iLQR) solver. It shows that an analytical derivative can be obtained through a backward pass resembling a modified iLQR solver.
2. Imitation Learning Experiments: The approach is validated through experiments in imitation learning on pendulum and cart-pole domains, demonstrating that the MPC-based policies are more data-efficient compared to traditional neural network approaches. The experiments also highlight that the proposed approach can surpass conventional system identification methods when the expert dynamics cannot be accurately realized.
3. Addressing the Non-realizable Dynamic Models: In scenarios where the expert's dynamic parameters fall outside the model class being learned, the strategy surpasses standard System Identification (SysId) methods by directly optimizing the task-specific imitation loss, validating the benefit of integrating task-relevant feedback loops into the learning process.

Analytical and Empirical Observations

The paper's analytical approach stands out due to its robust computations and reduced complexity for obtaining gradients. The differences between the mainstream unrolled optimization approach and the fixed-point differentiation method are precisely highlighted, showing significant improvements in computational efficiency and performance consistency.

Further, empirical results show compelling improvements in sample efficiency and control policy accuracy when using differentiable MPC. The data from the experiments underscore the efficacy of using gradient-based tuning of MPC in capturing both cost functions and system dynamics, even under noisily observed dynamic scenarios or when the expert dynamics are "unrealizable."

Practical and Theoretical Implications

This paper has significant implications for both the theoretical landscape of RL and practical applications in control systems. From a theoretical standpoint, it enriches the RL domain with a hybrid control paradigm that integrates the rigor of analytic derivatives in MPC with the flexibility of neural-based policy optimization.

Practically, this work provides a foundation for developing more data-efficient learning algorithms that can be applied in real-world robotics and autonomous systems. Its approach of using analytic derivatives promotes robust policy certification and systematic analysis of learned dynamics and objectives, paving the path for more reliable autonomous control architectures.

Moving forward, potential exploration areas involve extending these methodologies to handle stochastic environments, integrate with multi-agent systems, or allow for more comprehensive representation learning in high-dimensional state spaces. Additionally, further empirical validation in more complex, real-world scenarios could reinforce the practical viability of differentiable MPC in diverse AI applications.