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<p>The main aim of this paper is to extend the Bayesian approach to finding quadratic optimal control to a wider range of stochastic linear systems. These systems involve an unknown parameter in the drift term, which is observed through a noisy linear channel. The author demonstrates the effectiveness of the Bayesian strategy by comparing the cost it incurs with that of an optimal control that possesses complete knowledge of the parameter. The findings reveal that the Bayesian strategy minimizes the worst-case multiplicative regret. Furthermore, the author provides a proof that the corresponding adaptive scheme is optimal when the unknown system parameter belongs to an infinite space. This result further validates the effectiveness of the Bayesian strategy in handling systems with unknown parameters. In summary, this paper contributes to the generalization of the Bayesian strategy for the optimal control in stochastic linear systems with unknown parameters. It also establishes a theoretical basis for its optimality.</p>

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Optimal Control with Learning on the Fly from Finite to Infinite-Dimensional Systems

  • 期刊论文

  • 发表日期：

    2026年7月13日

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  • Feifei Miao

摘要

The main aim of this paper is to extend the Bayesian approach to finding quadratic optimal control to a wider range of stochastic linear systems. These systems involve an unknown parameter in the drift term, which is observed through a noisy linear channel. The author demonstrates the effectiveness of the Bayesian strategy by comparing the cost it incurs with that of an optimal control that possesses complete knowledge of the parameter. The findings reveal that the Bayesian strategy minimizes the worst-case multiplicative regret. Furthermore, the author provides a proof that the corresponding adaptive scheme is optimal when the unknown system parameter belongs to an infinite space. This result further validates the effectiveness of the Bayesian strategy in handling systems with unknown parameters. In summary, this paper contributes to the generalization of the Bayesian strategy for the optimal control in stochastic linear systems with unknown parameters. It also establishes a theoretical basis for its optimality.