Controlling unknown linear dynamics with almost optimal regret

• Jacob Carruth ^[1] ; Maximilian F. Eggl ^[2] ; Charles Fefferman ^[1] ; Clarence W. Rowley ^[1]
  1. [1] Princeton University

     Princeton University

     Estados Unidos

     
  2. [2] University of Bonn

     University of Bonn

     Kreisfreie Stadt Bonn, Alemania

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 41, Nº 2, 2025, págs. 745-806
• Idioma: inglés
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• Resumen

  • Here and in a companion paper, we consider a simple control problem in which the underlying dynamics depend on a parameter a that is unknown and must be learned. In this paper, we assume that a can be any real number and we do not assume that we have a prior belief about a. We seek a control strategy that minimizes a quantity called the regret. Given any ε>0, we produce a strategy that minimizes the regret to within a multiplicative factor of (1+ε).