We study gradient descent (GD) and its variants for convex objectives satisfying <inline-formula> <tex-math notation="LaTeX">$(L_{0},L_{1})$ </tex-math></inline-formula>-smoothness. Our analysis reveals a fast initial regime that is hidden by worst-case sublinear bounds: while <inline-formula> <tex-math notation="LaTeX...
A. Lobanov, A. Gasnikov, Eduard A. Gorbunov et al.· IEEE Access· 0 citations
The method, certificate transport, keeps a strongly convex lower model of a single slice and uses it as a prior for a short accelerated run on the next slice and shows that the inner problems need not be solved accurately.
An accelerated decentralized method with matching minimax guarantees in the smooth strongly convex regime is developed and extended to smooth and nonsmooth convex objectives and experiments confirm the predicted dependence on cross-channel geometry and network conditioning.
Ewsey R. Obzherin, I. Khomchenko, Natalia Shelegeda et al.· 0 citations
We study convex-concave minimax optimization problems with bilinear coupling of the form $\min_{x\in \mathcal X}\max_{y\in \mathcal Y} \; f(x)+\langle y,\mathbf{B}x\rangle-g(y),$ where the functions $f$ and $g$ have H\"older continuous (sub)gradients. This setting covers a broad range of regimes, from nonsmooth problem...
Nhat Trung Nguyen, A. Gasnikov· 0 citations
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