Colloquium Series: John Duchi

Our upcoming event for the Statistics Department Colloquium Series is scheduled for Monday, September 9 from 12:00 – 1:00pm (ET) and will be an in-person presentation Science Center Rm. 316. Lunch will be provided to guests following the talk. This week's speaker will be John Duchi of the Statistics and Electrical Engineering departments at Stanford University.

Geometry, Computation, and Optimality in Stochastic Optimization

We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and adaptive-gradient methods are (minimax) optimal and, conversely, when nonlinear updates—such as those mirror descent employs—are necessary for optimal convergence. When the constraint set is quadratically convex, diagonally pre conditioned stochastic gradient methods are minimax optimal. We provide quantitative converses showing that the “distance” of the underlying constraints from quadratic convexity determines the suboptimality of subgradient methods. These results apply, for example, to any `p-ball for p < 2, and the computation/accuracy tradeoffs they demonstrate exhibit a striking analogy to those in Gaussian sequence models.