For permutation-invariant quadratics, random-permutation coordinate descent has a provably smaller contraction-rate upper bound than random coordinate descent's lower bound on every instance.
Curiously fast convergence of some stochastic gradient descent algorithms
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Provable Benefit of Random Permutations over Uniform Sampling in Stochastic Coordinate Descent
For permutation-invariant quadratics, random-permutation coordinate descent has a provably smaller contraction-rate upper bound than random coordinate descent's lower bound on every instance.