Today’s real-world problems are complex and large, often with an overwhelmingly large number of unknown variables which render them doomed to the so-called “curse of dimensionality”. For instance, in machine learning, it is important to obtain simple, interpretable, and parsimonious models of high-dimensional and noisy data. As another example, in large-scale dynamic systems, a long standing question is how to efficiently design distributed control policies for unknown and interconnected systems.
Our research is centered around two main objectives: (1) to model these problems as tractable optimization problems; and (2) to develop structure-aware and scalable computational methods for solving these optimization problems that come equipped with certifiable optimality guarantees. At the core of our research is to show that exploiting hidden structures in these problems—such as graph-induced or spectral sparsity—is a key game-changer in the pursuit of massively scalable and guaranteed computational methods.