Jacob Sacks

Jacob Sacks, Byron Boots

Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of MPC, often through learning or fine-tuning the dynamics or cost function. In contrast, we focus on learning to optimize more effectively. In other words, to improve the update rule within MPC. We show that this can be particularly useful in sampling-based MPC, where we often wish to minimize the number of samples for computational reasons. Unfortunately, the cost of computational efficiency is a reduction in performance; fewer samples results in noisier updates. We show that we can contend with this noise by learning how to update the control distribution more effectively and make better use of the few samples that we have. Our learned controllers are trained via imitation learning to mimic an expert which has access to substantially more samples. We test the efficacy of our approach on multiple simulated robotics tasks in sample-constrained regimes and demonstrate that our approach can outperform a MPC controller with the same number of samples.

Jacob Sacks, Rwik Rana, Kevin Huang et al.

A major challenge in robotics is to design robust policies which enable complex and agile behaviors in the real world. On one end of the spectrum, we have model-free reinforcement learning (MFRL), which is incredibly flexible and general but often results in brittle policies. In contrast, model predictive control (MPC) continually re-plans at each time step to remain robust to perturbations and model inaccuracies. However, despite its real-world successes, MPC often under-performs the optimal strategy. This is due to model quality, myopic behavior from short planning horizons, and approximations due to computational constraints. And even with a perfect model and enough compute, MPC can get stuck in bad local optima, depending heavily on the quality of the optimization algorithm. To this end, we propose Deep Model Predictive Optimization (DMPO), which learns the inner-loop of an MPC optimization algorithm directly via experience, specifically tailored to the needs of the control problem. We evaluate DMPO on a real quadrotor agile trajectory tracking task, on which it improves performance over a baseline MPC algorithm for a given computational budget. It can outperform the best MPC algorithm by up to 27% with fewer samples and an end-to-end policy trained with MFRL by 19%. Moreover, because DMPO requires fewer samples, it can also achieve these benefits with 4.3X less memory. When we subject the quadrotor to turbulent wind fields with an attached drag plate, DMPO can adapt zero-shot while still outperforming all baselines. Additional results can be found at https://tinyurl.com/mr2ywmnw.

Nolan Wagener, Ching-An Cheng, Jacob Sacks et al.

Model predictive control (MPC) is a powerful technique for solving dynamic control tasks. In this paper, we show that there exists a close connection between MPC and online learning, an abstract theoretical framework for analyzing online decision making in the optimization literature. This new perspective provides a foundation for leveraging powerful online learning algorithms to design MPC algorithms. Specifically, we propose a new algorithm based on dynamic mirror descent (DMD), an online learning algorithm that is designed for non-stationary setups. Our algorithm, Dynamic Mirror Descent Model Predictive Control (DMD-MPC), represents a general family of MPC algorithms that includes many existing techniques as special instances. DMD-MPC also provides a fresh perspective on previous heuristics used in MPC and suggests a principled way to design new MPC algorithms. In the experimental section of this paper, we demonstrate the flexibility of DMD-MPC, presenting a set of new MPC algorithms on a simple simulated cartpole and a simulated and real-world aggressive driving task. Videos of the real-world experiments can be found at https://youtu.be/vZST3v0_S9w and https://youtu.be/MhuqiHo2t98.

Brandon Amos, Ivan Dario Jimenez Rodriguez, Jacob Sacks et al.

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.