Here are some concrete research directions (but not limited to):
Nonconvex and/or nonsmooth optimization.
This topic includes:
1) designing efficient and provable smooth optimization algorithms for problems arising in machine learning and data science,
2) designing efficient nonsmooth optimization algorithms for robust estimation problems in machine learning and data science,
3) analyzing (not that scary) nonconvex problems, such as its global geometry, local geometry, and regularities,
4) applying advanced optimization techniques to a large class of applications arising in signal processing and computational imaging.
Reinforcement learning.
This direction is about to design and analyze efficient algorithms for (mainly) policy optimization.