Optimal agnostic control of unknown linear dynamics in a bounded parameter range

  • Jacob Carruth

    Princeton University, Princeton, USA
  • Maximilian F. Eggl

    University of Bonn, Bonn, Germany
  • Charles Fefferman

    Princeton University, Princeton, USA
  • Clarence W. Rowley

    Princeton University, Princeton, USA
Optimal agnostic control of unknown linear dynamics in a bounded parameter range cover
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Abstract

Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. In this paper, we assume that is bounded, i.e., that , and we study two variants of the control problem. In the first variant, Bayesian control, we are given a prior probability distribution for and we seek a strategy that minimizes the expected value of a given cost function. Assuming that we can solve a certain PDE (the Hamilton–Jacobi–Bellman equation), we produce optimal strategies for Bayesian control. In the second variant, agnostic control, we assume nothing about and we seek a strategy that minimizes a quantity called the regret. We produce a prior probability distribution supported on a finite subset of so that the agnostic control problem reduces to the Bayesian control problem for the prior .

Cite this article

Jacob Carruth, Maximilian F. Eggl, Charles Fefferman, Clarence W. Rowley, Optimal agnostic control of unknown linear dynamics in a bounded parameter range. Rev. Mat. Iberoam. 41 (2025), no. 2, pp. 651–744

DOI 10.4171/RMI/1510