On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control

• URL: http://arxiv.org/abs/2306.01914v2
• Date: Tue, 3 Sep 2024 17:47:09 GMT
• Title: On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control
• Authors: Daniel Pfrommer, Swati Padmanabhan, Kwangjun Ahn, Jack Umenberger, Tobia Marcucci, Zakaria Mhammedi, Ali Jadbabaie,
• Abstract summary: We show how a smoothed expert can be designed for a general class of systems. We prove on the optimality gap of the analytic center associated with a convex Lipschitz function.
• Score: 27.609098229134
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. At the crux of this theoretical guarantee on smoothness is a new lower bound we prove on the optimality gap of the analytic center associated with a convex Lipschitz function, which we hope could be of independent interest. We validate our theoretical findings via experiments, demonstrating the merits of our smoothing approach over randomized smoothing.

Related papers

• Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control [27.609098229134]
  We show how a smoothed expert controller can be designed for a general class of systems. We show that barrier MPC achieves theoretically optimal error-to-smoothness tradeoff along some direction.
  arXiv  Detail & Related papers  (2024-10-01T16:52:23Z)
• Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior [51.60683890503293]
  We propose a theoretical framework for studying behavior cloning of complex expert demonstrations using generative modeling. We show that pure supervised cloning can generate trajectories matching the per-time step distribution of arbitrary expert trajectories.
  arXiv  Detail & Related papers  (2023-07-27T04:27:26Z)
• Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations [50.37808220291108]
  This paper addresses learning safe output feedback control laws from partial observations of expert demonstrations. We first propose robust output control barrier functions (ROCBFs) as a means to guarantee safety. We then formulate an optimization problem to learn ROCBFs from expert demonstrations that exhibit safe system behavior.
  arXiv  Detail & Related papers  (2021-11-18T23:21:00Z)
• Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
  Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
  arXiv  Detail & Related papers  (2021-05-17T08:36:18Z)
• Closing the Closed-Loop Distribution Shift in Safe Imitation Learning [80.05727171757454]
  We treat safe optimization-based control strategies as experts in an imitation learning problem. We train a learned policy that can be cheaply evaluated at run-time and that provably satisfies the same safety guarantees as the expert.
  arXiv  Detail & Related papers  (2021-02-18T05:11:41Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)
• Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting [91.43582419264763]
  We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model.
  arXiv  Detail & Related papers  (2020-03-12T19:56:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.