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arXiv · 2506.08031

Stochastic Krasnosel skii-Mann Iterations in Banach Spaces with Bregman Distances

Saeed Hashemi Sababe·Ehsan Lotfali Ghasab
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Abstract

We propose a generalization of the stochastic Krasnoselskil-Mann $(SKM)$ algorithm to reflexive Banach spaces endowed with Bregman distances. Under standard martingale-difference noise assumptions in the dual space and mild conditions on the distance-generating function, we establish almost-sure convergence to a fixed point and derive non-asymptotic residual bounds that depend on the uniform convexity modulus of the generating function. Extensions to adaptive Bregman geometries and robust noise models are also discussed. Numerical experiments on entropy-regularized reinforcement learning and mirror-descent illustrate the theoretical findings.

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Saeed Hashemi Sababe, Ehsan Lotfali Ghasab. 2025-06-02. Stochastic Krasnosel skii-Mann Iterations in Banach Spaces with Bregman Distances. https://arxiv.org/abs/2506.08031

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