Theory / Machine Learning Talk
ASA Conference Room 6115 (new location) - Gates Hillman Centers
LORENZO ORECCHIA , Assistant Professor
First-Order Optimization and the Calculus of Variations
We present a novel approach to analyze and design first-order methods for convex optimization via the calculus of variations. Specifically, we show that the continuous-time dynamics underlying these methods arise as the unique solutions of the minimization of natural convex functionals over the space of absolutely continuous paths from a given starting point. While previous work has characterized these continuous-time dynamics as critical points of certain functionals, i.e., solutions to Euler-Lagrange equations, our work is the first to give a convex formulation of these functionals. An interesting upshot of this work is that the problem of designing continuous-time first-order methods for convex optimization is itself a convex optimization problem.
Faculty Host: Gary L. Miller
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