Competitive-Ratio and Regret-Optimal Control with General Weights

Oron Sabag, Sahin Lale, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


Motivated by the online policy design approaches in learning theory, new controller design paradigms such as competitive-ratio and regret-optimal control have been recently proposed as alternatives to the classical H2 and H controllers. These metrics respectively consider the performances against a clairvoyant controller, which has access to future disturbances, in terms of ratio and difference. Even though the prior works on regret-optimal control provide its exact solution, in the competitive-ratio setting the solution is only provided for the suboptimal problem. In this work, we give the first exact solution to the optimal competitive-ratio control problem and present an explicit construction of the optimal competitive-ratio controller. A key technique that underpins our explicit solution is a reduction of the competitive-ratio control problem to the Nehari extension problem (similar to the regret-optimal control setting). The resulting optimal competitive-ratio controller is given by an explicit state space and the state-feedback law that is inherited from the H_2 controller. Inspired by this explicit solution, we generalize regret-optimal control to have weight functions on the state, input, and noise sequences and show that competitive-ratio control is an instance of this general framework. The utilization of weight functions allow penalization of particular sequences, but still enjoying the explicit and optimal solution for the regret-optimal control problem.

Original languageAmerican English
Title of host publication2022 IEEE 61st Conference on Decision and Control, CDC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665467612
StatePublished - 2022
Event61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico
Duration: 6 Dec 20229 Dec 2022

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference61st IEEE Conference on Decision and Control, CDC 2022

Bibliographical note

Publisher Copyright:
© 2022 IEEE.


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