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• W3035237169 abstract "Motivated by the Dikin walk, we develop aspects of the interior-point theory for sampling in high dimension. Specifically, we introduce the notions of strong self-concordance and symmetry for a barrier. These properties imply that the Dikin walk defined using a strongly self-concordant barrier with symmetry parameter ν mixes in Õ(nν) steps from a warm start for a convex body in ℝ n . For many natural barriers, ν is roughly bounded by ν, the standard self-concordance parameter. We also show that these properties hold for the Lee-Sidford barrier. As a consequence, we obtain the first walk that mixes in Õ(n 2) steps for an arbitrary polytope in ℝ n . Strong self-concordance for other barriers leads to an interesting (and unexpected) connection — for the universal and entropic barriers, it is implied by the KLS conjecture." @default.
• W3035237169 created "2020-06-19" @default.
• W3035237169 creator A5024980585 @default.
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• W3035237169 date "2020-06-22" @default.
• W3035237169 modified "2023-10-18" @default.
• W3035237169 title "Strong self-concordance and sampling" @default.
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• W3035237169 doi "https://doi.org/10.1145/3357713.3384272" @default.
• W3035237169 hasPublicationYear "2020" @default.
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