Derives novel high-dimensional concentration inequalities for vector-valued Markov chain martingales and applies them to TD learning for consistency guarantees matching asymptotic variance up to logs and O(T^{-1/4} log T) Gaussian approximation rate.
In combination, the triangle inequality reveals dC( √ T∆T ,N(0, eΛ⋆))≥d C(N(0, eΛT ),N(0, eΛ⋆))−d C( √ T∆T ,N(0, eΛT )) ≳O(T α−1)−O(T − 1 4 ) ≳O(T α−1)≳O(T − 1 4 )
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Uncertainty quantification for Markov chain induced martingales with application to temporal difference learning
Derives novel high-dimensional concentration inequalities for vector-valued Markov chain martingales and applies them to TD learning for consistency guarantees matching asymptotic variance up to logs and O(T^{-1/4} log T) Gaussian approximation rate.