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We study the last iterate of standard asynchronous Q-learning from a single trajectory of a finite Markov decision process. The trajectory follows a fixed behavior policy whose state--action chain is irreducible and may be periodic. For discount factor $\gamma$, write $H=(1-\gamma)^{-1}$, and let $\mu_{\min}$ be the mi...
The framework connects benchmark performance to experimentally actionable diagnoses of reservoir encoding, measurement choice, classical representation, and shot allocation and introduces task-resolved Fisher spectroscopy, in which prediction targets define orthonormal score coordinates on the stationary distribution o...
A local asymptotic theory is developed for the estimated return CDF over $T^{-1/2}$-neighborhoods of finitely many thresholds, together with its bootstrap analogue that justifies bootstrap inference for smooth statistical functionals, including variance, CVaR, expected shortfall, and expectiles.
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