A common and powerful way to think about stochastic systems is through the lens of stochastic kernels, which are measurable maps from the state space (possibly also the control space) to the space of probability measures over the state space. Motivated by the fact that we live in a data-rich world, where data can be used to generate approximations for the underlying stochastic kernel, we are exploring how to develop control policies that are robust against kernels that belong to ambiguity sets, which are themselves constructed using the available data. Together with my collaborator Prof. Ashish Hota, IIT Kharagpur, we have recently studied well-posedness of dynamic programming under kernel-based ambiguity sets. Relevant paper is:
- L. Romao, A. R. Hota, A. Abate. “Distributionally Robust Optimal and Safe Control for Stochastic Systems via Kernel Conditional Mean Embedding”. Technical report.