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.
Rates of Convergence in the Central Limit Theorem for Markov Chains, with an Application to TD learning
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Establishes non-asymptotic and functional central limit theorems for asynchronous averaged Q-learning with explicit rates depending on iterations, state-action space, discount factor, and exploration quality.
Proves the first fully non-asymptotic bound on the accuracy of multiplier bootstrap for constructing confidence sets from Polyak-Ruppert SGD iterates, achieving convex-distance rates up to 1/sqrt(n) under regularity conditions.
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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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Central Limit Theorems for Asynchronous Averaged Q-Learning
Establishes non-asymptotic and functional central limit theorems for asynchronous averaged Q-learning with explicit rates depending on iterations, state-action space, discount factor, and exploration quality.
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Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent
Proves the first fully non-asymptotic bound on the accuracy of multiplier bootstrap for constructing confidence sets from Polyak-Ruppert SGD iterates, achieving convex-distance rates up to 1/sqrt(n) under regularity conditions.