Currently I'm especially interested in (i) the interplay between convexity and randomness in optimization, and (ii) inference problems on random graphs.
NEW: polynomial-time algorithm for bandit convex optimization
From July 2014 to July 2016 with various co-authors at MSR we dedicated a lot of energy to bandit convex optimization. The end product is a new efficient algorithm. To learn more about it I recommend to first take a look at this [youtube video], then these 3 blog posts ([part 1], [part 2], [part 3]), and finally [the paper] itself.