The paper proves the first optimal O(n^{-1/2}) Wasserstein-1 CLT rates for locally dependent sequences and geometrically ergodic Markov chains, plus new W_p rates for p greater than or equal to 2 under mild moments, with an application to U-statistics.
Bridging the gap between constant step size stochastic gradient descent and markov chains
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Combining random reshuffling and Richardson-Romberg extrapolation yields cubic bias refinement and better MSE for constant-step SGD on structured non-monotone variational inequalities.
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Wasserstein-p Central Limit Theorem Rates: From Local Dependence to Markov Chains
The paper proves the first optimal O(n^{-1/2}) Wasserstein-1 CLT rates for locally dependent sequences and geometrically ergodic Markov chains, plus new W_p rates for p greater than or equal to 2 under mild moments, with an application to U-statistics.
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Shuffling the Data, Stretching the Step-size: Sharper Bias in constant step-size SGD
Combining random reshuffling and Richardson-Romberg extrapolation yields cubic bias refinement and better MSE for constant-step SGD on structured non-monotone variational inequalities.