Robust Regression for Safe Exploration in Control

Abstract

We study the problem of safe learning and exploration in sequential control problems. The goal is to safely collect data samples from an operating environment to learn an optimal controller. A central challenge in this setting is how to quantify uncertainty in order to choose provably-safe actions that allow us to collect useful data and reduce uncertainty, thereby achieving both improved safety and optimality. To address this challenge, we present a deep robust regression model that is trained to directly predict the uncertainty bounds for safe exploration. We then show how to integrate our robust regression approach with model-based control methods by learning a dynamic model with robustness bounds. We derive generalization bounds under domain shifts for learning and connect them with safety and stability bounds in control. We demonstrate empirically that our robust regression approach can outperform conventional Gaussian process (GP) based safe exploration in settings where it is difficult to specify a good GP prior.