A Banach-Space Theory of Markovian Halpern Iteration for Non-Expansive Maps
We study stochastic approximation of fixed points of a non-expansive operator $T$ when the oracle samples originate from a continuing Markovian trajectory. A direct block-minibatch implementation of Halpern iteration attains an expected last-iterate residual of order $O(\log N/N)$, but accrues a substantive complexity of $\tilde O(ε^{-5})$ Markovian samples. We therefore introduce a variance-reduced Markovian PAGE-Halpern method whose refresh and same-state difference blocks are analyzed through the Poisson equation. In Hilbert spaces, the cocoercivity of $I-T$ results in an $O(ε^{-3})$ sample complexity. Our main result extends this construction to a general finite-dimensional Banach spa...
| Authors | Ege C. Kaya, Arda Fazla, M. Berk Sahin et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 August 2026 |
| Last updated at source | 25 September 2026 |
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