Regret Bounds for the Adaptive Control of Linear Quadratic Systems
published: Aug. 2, 2011, recorded: July 2011, views: 3792
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
We study the average cost Linear Quadratic (LQ) problem with unknown model parameters, also known as the adaptive control problem in the control community. We design an algorithm and prove that its regret up to time T is O(√T) apart from logarithmic factors. Unlike many classical approaches that use a forced-exploration scheme to provide the sufficient exploratory information for parameter estimation, we construct a high-probability confidence set around the model parameters and design an algorithms that plays optimistically with respect to this confidence set. The construction of the confidence set is based on the new results from online least-squares estimation and leads to improved worst-case regret bound for the proposed algorithm. To best of our knowledge this is the the first time that a regret bound is derived for the LQ problem.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !