I am interested in Mathematical Learning and Control Theory, specifically in settings where we have limited access to training data. One line studies control problems in which the agent must learn an optimal control strategy with little data and little time available. Our motivating example is the success of pilots learning in real time to fly and safely land an airplane after it has been severely damaged. In contrast to the previous control theory literature that focuses mostly on asymptotics as the time horizon tends to infinity, we consider problems posed over a finite time horizon. We study different versions of the problem, with varying assumptions on the dynamics and prior information. We are particularly interested in agnostic problems, where the parameters of the underlying system dynamics are a priori completely unknown. Another line of ongoing work studies active learning approaches for interpolation and approximation of smooth functions, where the acquisition of geometric information guides our learning strategy.
- J. Carruth, M. F. Eggl, C. L. Fefferman, C. W. Rowley, M. Weber (2021): Controlling Unknown Linear Dynamics with Bounded Multiplicative Regret. arXiv:2109.06350 Under Review. [pdf]
- C. L. Fefferman, B. Guillen Pegueroles, C. W. Rowley, M. Weber (2021): Optimal control with learning on the fly: a toy problem. Revista Matemática Iberoamericana 37 (1). [pdf]