“Non-convex optimization when the solution is not unique: a kaleidoscope of favorable conditions”
Friday March 10, 2023 | Time 15:00 CET
Classical optimization algorithms can see their local convergence rates deteriorate when the Hessian at the optimum is singular. The latter is inescapable when the optima are non-isolated. Yet, several algorithms behave perfectly nicely even when optima form a continuum (e.g., due to overparameterization). This has been studied through various lenses, including the Polyak-Lojasiewicz inequality, Quadratic Growth, the Error Bound, and (less so) through a Morse-Bott property. I will present work with Quentin Rebjock showing tight links between all of these.
Nicolas Boumal is assistant professor of mathematics at EPFL, and an associate editor of the journal Mathematical Programming. He explores geometry, symmetry and statistics in optimization to tackle nonconvexity, as part of an ERC Starting Grant funded by SERI. Nicolas has contributed to several modern theoretical advances in Riemannian optimization. He wrote a book on this topic, and is a lead-developer of the award-winning toolbox Manopt, which facilitates experimentation with optimization on manifolds.