Year: 2022
Type: preprint
Abstract: We study nonsmooth convex minimization over a compact convex set without projections. For a globally $L$-Lipschitz objective, optimistic primal-dual updates give error at most $2LD/\sqrt{T}$ after $T$ iterations, where $D$ is the set's diameter. Each iteration uses at most one linear optimization call and one subgradient query at a point that may lie outside the feasible set. For objectives that are $μ$-strongly convex on the feasible set, we present a direct method with error at most $32ρ^2L^2/[μ(T+1)]$. It uses a local linear optimization oracle with expansion factor $ρ$ and subgradients of norm at most $L$ queried only at feasible points. The method requires neither restarts nor advance knowledge of $T$. We give self-contained proofs and a short restart argument for the convex variant of the Garber-Hazan algorithm that removes the logarithmic factor from their error bound.
Source: arXiv (Cornell University)
Authors: Asgari, Kamiar, Neely, Michael J.
Institution: University of Southern California
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4290858305