Title: Kernel Distributionally Robust Optimal Control

Abstract: We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the state evolution into an associated reproducing kernel Hilbert space. Our key idea lies in combining conditional mean embedding with the maximum mean discrepancy distance to construct an ambiguity set, and then design a robust control policy using techniques from distributionally robust optimization. The main theoretical contribution of this paper is to leverage functional analytic tools to prove that optimal policies for this infinite-dimensional min-max problem are Markovian and deterministic. Additionally, we discuss approximation schemes based on state and input discretization to make the approach computationally tractable.

Biography: Ashish R. Hota is an Assistant Professor in the Department of Electrical Engineering at Indian Institute of Technology (IIT), Kharagpur. He was a postdoctoral researcher at the Automatic Control Laboratory, ETH Zurich in 2018. He received his Ph.D. from Purdue University in 2017, and his B.Tech and M.Tech (dual degree) from Indian Institute of Technology (IIT), Kharagpur, in 2012, all in Electrical Engineering. From 2012 to 2014, he was a research assistant at the University of Waterloo, Canada. He received the Indian National Academy of Engineering (INAE) Young Associate Award in 2023, Outstanding Graduate Researcher Award from the College of Engineering, Purdue University in 2017, and the Institute Silver Medal from IIT Kharagpur in 2012. His research interests lie in the areas of (i) game theory and behavioral decision theory, (ii) stochastic optimization, control and learning and (iii) resilience and security of network systems.