Feedback-driven decision-making systems are at the emerging frontier of machine learning applications. Upcoming applications of societal consequence, such as self-driving vehicles and smartwatch-based health interventions, have to contend with the challenge of operating in reactive stateful environments. In this talk, I will describe my work on designing principled robust algorithms for feedback-driven learning, with provable guarantees on computational and statistical efficiency.

First, I will introduce an efficient instance-optimal algorithm for control in the presence of adversarial disturbances. Beyond the realm of both stochastic and robust control, such a data-driven notion of optimality combines worst-case guarantees with a promise of exceptional performance on benign instances. Moving on to prediction, I will present a computationally and statistically efficient forecasting strategy for latent-state dynamical systems exhibiting long term dependencies, mitigating the statistical challenge of learning with correlated samples, and the computational difficulties associated with a non-convex maximum likelihood objective. To conclude, I will discuss some practically relevant fundamental questions at the intersection of machine learning, optimization, and control that have the potential to unlock real progress in downstream applications.