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arXiv · 2309.07091

Optimal adaptive control with separable drift uncertainty

Samuel N. Cohen·Christoph Knochenhauer·Alexander Merkel
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Abstract

We consider a problem of stochastic optimal control with separable drift uncertainty in strong formulation on a finite horizon. The drift coefficient of the state $Y^{u}$ is multiplicatively influenced by an unknown random variable $\lambda$, while admissible controls $u$ are required to be adapted to the observation filtration. Choosing a control actively influences the state and information acquisition simultaneously and comes with a learning effect. The problem, initially non-Markovian, is embedded into a higher-dimensional Markovian, full information control problem with control-dependent filtration and noise. To that problem, we apply the stochastic Perron method to characterize the value function as the unique viscosity solution to the HJB equation, explicitly construct $\varepsilon$-optimal controls and show that the values of strong and weak formulations agree. Numerical illustrations show a significant difference between the adaptive control and the certainty equivalence control.

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Samuel N. Cohen, Christoph Knochenhauer, Alexander Merkel. 2023-09-13. Optimal adaptive control with separable drift uncertainty. https://arxiv.org/abs/2309.07091

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