3 accepted papers
Mean-field Langevin dynamics (MLFD) is a class of interacting particle methods that tackle convex optimization over probability measures on a manifold, which are scalable, versatile, and enjoy computational guarantees. However, some important problems -- such as risk minimization for infinite width…
We study the convergence to local Nash equilibria of gradient methods for two-player zero-sum differentiable games. It is well-known that, in the continuous-time setting, such dynamics converge locally when $S \succ 0$ and may diverge when $S=0$, where $S\succeq 0$ is the symmetric part of the Jacob…
We provide matching upper and lower bounds of order $\sigma^2/\log(d/n)$ for the prediction error of the minimum $\ell_1$-norm interpolator, a.k.a. basis pursuit. Our result is tight up to negligible terms when $d \gg n$, and is the first to imply asymptotic consistency of noisy minimum-norm interpo…