Consider the following two-person mixed strategy game of a probabilist against Nature with respect to the parameters (f,B,π), where f is a convex function satisfying certain regularity conditions, B is either the set {L_i}_{i=1}^{n} or its convex hull with each L_i being a Markov infinitesimal generator on a finite state space X and π is a given positive discrete distribution on X. The probabilist chooses a prior measure μ within the set of probability measures on B denoted by P(B) and picks a L∈B at random according to μ, whereas Nature follows a pure strategy to select M∈L(π), the set of ππ-reversible Markov generators on X. Nature pays an amount D_f(M||L), the f-divergence from L to M, to the probabilist. We prove that a mixed strategy Nash equilibrium always exists, and establish a minimax result on the expected payoff of the game. This also contrasts with the pure strategy version of the game where we show a Nash equilibrium may not exist. To find approximately a mixed strategy Nash equilibrium, we propose and develop a simple projected subgradient algorithm that provably converges with a rate of O(1/sqrt{t}), where t is the number of iterations. In addition, we elucidate the relationships of Nash equilibrium with other seemingly disparate notions such as weighted information centroid, Chebyshev center and Bayes risk. This talk highlights the powerful interplay and synergy between modern Markov chains theory and geometry, information theory, game theory, optimization and mathematical statistics. This is based on a joint work with Geoffrey Wolfer (RIKEN AIP), and the paper can be found in https://arxiv.org/abs/2310.04115

Michael Choi received his Ph.D. from the School of Operations Research and Information Engineering at Cornell University and his Bachelor of Science degree in Actuarial Science with first class honors at The University of Hong Kong. He is currently an assistant professor at the Department of Statistics and Data Science with a joint appointment at the Yale-NUS College at the National University of Singapore. He is also affiliated with the Institute of Operations Research and Analytics (iORA). His research interests revolve around Markov chains and Markov processes theory and their applications in various areas including but not limited to statistical physics, information theory, stochastic optimization and Bayesian statistics, along with a particular focus on the design and analysis of stochastic algorithms in these areas.

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg