In finite-horizon noisy LQ control, the policy gradient estimator and its objective cost are claimed to be asymptotically normal, and online bootstrapped confidence intervals are claimed valid with quantile error n^{-1/4}.
Reinforcement learning applied to linear quadratic regulation
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Toward Optimal Statistical Inference in Noisy Linear Quadratic Reinforcement Learning over a Finite Horizon
In finite-horizon noisy LQ control, the policy gradient estimator and its objective cost are claimed to be asymptotically normal, and online bootstrapped confidence intervals are claimed valid with quantile error n^{-1/4}.