Samuel Cohen - Optimal adaptive control with separable drift uncertainty
| Dates: | 6 March 2024 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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Samuel Cohen (University of Oxford) will speak at the Probability seminar.
We consider a problem of stochastic optimal control with drift uncertainty, in a strong formulation on a finite horizon. The drift coefficient of the state is multiplicatively influenced by an unknown random variable, while admissible controls are required to be adapted to the observation filtration. This raises issues, as choosing a control actively influences the state and information acquisition, leading to a learning effect, corresponding to a continuous time version of the exploration/exploitation trade-off. As the filtration is controlled, the dynamic programming principle is difficult to establish, and the class of admissible controls is subtle. We apply the stochastic Perron method to characterize the value function as the unique viscosity solution to an HJB equation, explicitly construct ?-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/model predictive control.
Based on joint work with Alexander Merkel and Christoph Knochenhauer.
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