77 citations · 318 across the 57 of their papers we have counts for
8 papers · 1 filter
Inexact alternating projections on nonconvex sets
Dmitriy Drusvyatskiy, Adrian S. Lewis
Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a…
Graphical Convergence of Subgradients in Nonconvex Optimization and Learning
Damek Davis, Dmitriy Drusvyatskiy
We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex…
Stochastic model-based minimization under high-order growth
Damek Davis, Dmitriy Drusvyatskiy, Kellie J. MacPhee
Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the…
Stochastic subgradient method converges on tame functions
Damek Davis, Dmitriy Drusvyatskiy, Sham Kakade +1
This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity? We prove that the stochastic s…
Subgradient methods for sharp weakly convex functions
Damek Davis, Dmitriy Drusvyatskiy, Kellie J. MacPhee +1
Subgradient methods converge linearly on a convex function that grows sharply away from its solution set. In this work, we show that the same is true for sharp functions that are o…
Stochastic model-based minimization of weakly convex functions
Damek Davis, Dmitriy Drusvyatskiy
We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximati…