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Potential-Function Proofs for First-Order Methods

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arxiv 1712.04581 v3 pith:HT5XDLPO submitted 2017-12-13 cs.LG cs.DSmath.OC

classification cs.LGcs.DSmath.OC
keywords methodsdescentfirst-orderpotential-functionproofsacceleratedargumentsconvergence
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This note discusses proofs for convergence of first-order methods based on simple potential-function arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants.

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    An edge-differentially-private algorithm approximates every cut of any unweighted n-vertex graph with error γ·cut + Õ(n^(13/12+o(1))), beating the previous polynomial-time bound of n^(5/4+o(1)).

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