论文标题
非专业图的随机定点迭代：收敛和误差边界
Stochastic fixed-point iterations for nonexpansive maps: Convergence and error bounds
论文作者
论文摘要
我们研究了众所周知的Krasnoselski-Mann迭代的随机扰动版本，用于计算有限维度规范空间中非专用图的固定点。我们讨论了随机噪声上的足够条件，并得出了一步，以确保迭代的迭代率几乎可以收敛，并得出固定点残差的非反应误差界限和收敛速率。我们的主要结果涉及可能存在无限制的变异的Martingale差异噪声。这支持了对平均奖励马尔可夫决策过程的强化学习的应用，我们为此建立了融合和渐近率。我们还深入分析了噪声具有均匀界限方差的情况，并以明确的可计算常数获得误差界。
We study a stochastically perturbed version of the well-known Krasnoselski--Mann iteration for computing fixed points of nonexpansive maps in finite dimensional normed spaces. We discuss sufficient conditions on the stochastic noise and stepsizes that guarantee almost sure convergence of the iterates towards a fixed point, and derive non-asymptotic error bounds and convergence rates for the fixed-point residuals. Our main results concern the case of a martingale difference noise with variances that can possibly grow unbounded. This supports an application to reinforcement learning for average reward Markov decision processes, for which we establish convergence and asymptotic rates. We also analyze in depth the case where the noise has uniformly bounded variance, obtaining error bounds with explicit computable constants.
