Abstract: Efficient computational methods with proven guarantees are essential for navigating the complexities and nonlinearities of real-world systems. While practitioners often rely on heuristic algorithms tailored for specific applications, their theoretical foundations remain unclear, limiting their use in safety-critical systems. This presentation aims to bridge this gap for non-convex machine learning problems, emphasizing the critical need for robustness in machine learning algorithms, particularly in safety-critical applications such as autonomous driving and power systems.

The talk will delve into cutting-edge developments in provably robust machine learning, presenting novel models supported by mathematical proofs of their robustness. Additionally, it will introduce optimization techniques designed to certify existing models. These methods leverage underlying problem structures to achieve state-of-the-art robustness and efficiency, promising breakthroughs in both reliability and computational effectiveness.

Abstract: To improve the efficiency, resiliency, and sustainability of power systems and to
address climate change issues, the operation of power systems is becoming data centric. Major
operational problems, such as security-constrained optimal power flow, contingency analysis,
and transient stability analysis, rely on the knowledge extracted from sensory data. The
manipulation of the data by a malicious actor can tamper with the operation of the grid, whose
consequences are catastrophic physical damages to the equipment and cascading failures. In
this talk, we first discuss the vulnerability of power systems to cyberattacks and faults, and then
study how to learn the model of a complex system in an adversarial environment and detect
possible attacks simultaneously. We develop different types of attack detection algorithms and
learning mechanisms, and demonstrate their performances on real-world data. We show that it
is possible to learn the model of a complex system in finite time even when the system is under
attack at almost all times.