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arXiv Machine Learning By Ege C. Kaya, Abolfazl Hashemi

A Finite-Iteration Theory for Asynchronous Categorical Distributional Temporal-Difference Learning

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The paper investigates the finite‑iteration behavior of exact asynchronous recursions used in categorical distributional temporal‑difference (TD) learning. It analyzes both scalar categorical TD in the Cramér geometry and multivariate signed‑categorical TD in the maximum mean discrepancy geometry, showing that these methods can be viewed as single‑state stochastic‑approximation recursions that contract in a block‑supremum norm. The authors develop a restricted‑domain theory, derive discounted bounds under i.i.d. and Markovian sampling, and extend the analysis to undiscounted fixed‑horizon policy evaluation with horizon‑stacked categorical methods under episodic sampling, thereby providing a unified non‑asymptotic analysis across various settings.

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