Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control
Recent work in imitation learning has shown that having an expert controller that is both suitably smooth and stable enables stronger guarantees on the performance of the learned controller. However, constructing such smoothed expert controllers for arbitrary systems remains challenging, especially in the presence of input and state constraints. As our primary contribution, we show how such a smoothed expert can be designed for a general class of systems using a log-barrier-based relaxation of a standard Model Predictive Control (MPC) optimization problem. Improving upon our previous work, we show that barrier MPC achieves theoretically optimal error-to-smoothness tradeoff along some direction. At the core of this theoretical guarantee on smoothness is an improved lower bound we prove on the optimality gap of the analytic center associated with a convex Lipschitz function, which we believe could be of independent interest. We validate our theoretical findings via experiments, demonstrating the merits of our smoothing approach over randomized smoothing.
Code (0)
등록된 구현이 없습니다.
Tasks
Imitation LearningModel Predictive ControlSimilar Papers 제목 키워드 기반
Safe Importance Sampling in Model Predictive Path Integral Control
We introduce the notion of importance sampling under embedded barrier state control, titled Safety Controlled Model Predictive Path Integral Control (SC-MPPI). For robotic systems operating in an environment with multipl…
On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control
Recent work in imitation learning has shown that having an expert controller that is both suitably smooth and stable enables stronger guarantees on the performance of the learned controller. However, constructing such sm…
Imitation LearningLearning TheoryModel Predictive ControlA Separation in Heavy-Tailed Sampling: Gaussian vs. Stable Oracles for Proximal Samplers
We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i.e., samplers that require only $O(\log(1/\varepsilon))$ versus $\Omega…
Mix-MaxEnt: Creating High Entropy Barriers To Improve Accuracy and Uncertainty Estimates of Deterministic Neural Networks
We propose an extremely simple approach to regularize a single deterministic neural network to obtain improved accuracy and reliable uncertainty estimates. Our approach, on top of the cross-entropy loss, simply puts an e…
Path Integral Methods with Stochastic Control Barrier Functions
Safe control designs for robotic systems remain challenging because of the difficulties of explicitly solving optimal control with nonlinear dynamics perturbed by stochastic noise. However, recent technological advances …