Controlling unknown linear dynamics with bounded multiplicative regret

• Jacob Carruth ^[1] ; Maximilian F. Eggl ^[3] ; Charles Fefferman ^[1] ; Clarence W. Rowley ^[1] ; Melanie Weber ^[2]
  1. [1] Princeton University

     Princeton University

     Estados Unidos

     
  2. [2] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
  3. [3] Institute for Physiological Chemistry, University of Mainz Medical Center

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº Extra 7, 2022 (Ejemplar dedicado a: Special issue in honor of Antonio Córdoba and José Luis Fernández), págs. 2185-2216
• Idioma: inglés
• DOI: 10.4171/RMI/1377
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• Resumen

  • We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We exhibit a control strategy which is optimal to within a multiplicative constant. While most authors find strategies which are successful as the time horizon tends to infinity, our strategy achieves lowest expected cost up to a constant factor for a fixed time horizon