Abstract:  In this talk, we will discuss several applications of bilevel optimization (BLO) in machine learning. Specifically, we will focus on BLO problems with constraints in the lower-level (LL) objective. For such problems, the standard implicit gradient-based approaches do not work in general. In our talk, we will discuss specific cases of constrained BLO and discuss approaches that allow us to develop (approximate) implicit gradient-based algorithms for such problems. Finally, we will demonstrate the performance of the proposed algorithms on signal processing and machine learning applications.