Our third roundtable discussion took place after Meisam Razaviyayn’s talk on “Learning via Non-Convex Min-Max games“. His talk slides can be found here.

The following note summarizes the roundtable discussion.

The topics were the Challenges and future of nonconvex optimization, and the landscape of Data Science at USC, the speaker’s home institution.

In the past three decades, the frontier of nonconvex optimization has changed significantly. Perhaps the broadest difference is a switch from general solution methods to focusing on developing methods tailored to solving specific problems. The host identified phase retrieval as an example of this, where careful transformations turn the problem into a convex one. Also he pointed out the importance of good initialization (e.g., the starting point) of various iterative algorithms in nonconvex optimization. The speaker broadly identified two current frontiers of nonconvex optimization, while an attendee added another: the broadest frontier is problems which are still nice, despite being nonconvex, either because they can be transformed into a convex problem, because they have many approximately equivalent solutions, or because a prudent choice of initial conditions leads to an effectively convex problem. The second frontier is problems where second and higher order information excludes local minima. The final frontier is problems where progressive convex relaxations approach the true solution. Finally, in some quarters there is an unfortunate movement towards “graduate student descent” which relies on painstaking tuning of parameters on the part of graduate students, but may not yield any great insight into the problem.

Our second topic was the state of Data Science at USC. They have a thriving community, with many initiatives coming from a broad class of departments from different schools, such as the Center for Artificial Intelligence in Society or the Machine Learning Research Center. There is also a lot of development in the medical school, as well as a new initiative in the journalism school. An attendee wondered if this leads to some redundancy, which is certainly a problem we need to consider for ourselves as we begin to have multiple centers as well. The speaker said that often these centers focused on somewhat different research areas, and when they shared similar areas, often the same faculty were involved in several of the groups simultaneously.

[Scribe: David Weber (GGAM)]