Fridays at 2:30 in Vincent Hall 002 (unless otherwise specified)
In the machine learning literature, one approach to "prediction" assumes that advice is available from a finite number of "experts." The best prediction in this setting is the one that "minimizes regret", i.e. minimizes the worst-case shortfall relative to the best performing expert. My talk discusses a particular problem of this type, which takes the form of a randomized-strategy two-player game. I'll explain how it can be addressed using ideas from optimal control and partial differential equations. The main idea is to consider a suitable continuum limit, and to characterize the value function using a nonlinear PDE. In some special cases, the value function even has an exact formula. As a consequence, one knows in those cases exactly how the experts' guidance should be weighted to obtain an optimal result. This is joint work with Nadejda Drenska. (host: F. Santosa)
(host: G. Lerman)