We study the long-time regime of the prediction with expert advice problems in both full information and adversarial bandit feedback settings. In the adversarial bandit feedback setting, we show that the problem leads to second order parabolic PDEs in the Wasserstein space. We establish the wellposedness of weak solutions for these PDEs and establish the connection between these PDEs, mean-field control, and filtering problems. Based on joint works with Ibrahim Ekren and Xin Zhang.

Bio:  Erhan Bayraktar, the holder of the Susan Smith Chair, is a full professor of Mathematics at the University of Michigan, where he has been since 2004. Professor Bayraktar's research is in stochastic analysis, control, applied probability, mean field games, machine learning, and mathematical finance.  He is a corresponding editor in the SIAM Journal on Control and Optimization and also serves on the editorial boards of Applied Mathematics and Optimization, Frontiers in Mathematical Finance, Mathematics of Operations Research, and Mathematical Finance. His research has also been continually funded by the National Science Foundation. In particular, he received a CAREER grant.  Professor Bayraktar has been the director of the Risk Management and Quantitative Finance Masters program since its inception in 2015. He has had 14 Ph.D. students and over 40 post-docs.