Prediction problems and second order equations

Job Candidate Talk
Thursday, December 15, 2022 - 11:00am for 1 hour (actually 50 minutes)
Skiles 006 or
Ibrahim Ekren – Florida State University – iekren@fsu.edu
Michael Damron

We study the long-time regime of the prediction with expert advice problem in both full information and adversarial bandit feedback setting. We show that with full information, the problem leads to second order parabolic partial differential equations in the Euclidean space. We exhibit solvable cases for this equation and discuss the optimal behavior of both agents. In the adversarial bandit feedback setting, we show that the problem leads to second order parabolic equations in the Wasserstein space which allows us to obtain novel regret bounds. Based on joint works with Erhan Bayraktar and Xin Zhang.