Anand Brahmbhatt will present his General Exam "Spectral and Improper Methods for Learning and Control of Dynamical Systems" on Friday, May 8, 2026 at 9:30 AM in CS 302. Committee Members: Elad Hazan (advisor), Mark Braverman, Sanjeev Arora Abstract: Classical control methods such as LQR provide powerful tools for known linear dynamical systems, but typically assume fixed quadratic costs and stochastic noise. In contrast, prior work in online control uses improper learning to handle changing convex cost functions and bounded oblivious adversarial disturbances, achieving optimal regret guarantees. In this talk, we revisit this line of work and show that, by imposing a suitable structural restriction on the policy class, one can design a spectral control algorithm that retains optimal regret while significantly improving computational efficiency, with per-iteration runtime scaling only polylogarithmically in the stability margin. We then describe extensions of this approach to partially observed systems and to bandit feedback, where only scalar cost information is available. Finally, we discuss how similar improper learning ideas extend to learning in nonlinear dynamical systems, yielding prediction guarantees via high-dimensional linear surrogates. Reading List: https://docs.google.com/document/d/1OLqfFM92wM6I1dQ5gbRBkZxCfgR_hOA8FS7mxuHs... Everyone is invited to attend the talk, and those faculty wishing to remain for the oral exam following are welcome to do so.