论文标题
随机Kaczmarz算法的最佳计划学习率
An optimal scheduled learning rate for a randomized Kaczmarz algorithm
论文作者
论文摘要
我们研究了学习率如何影响放松的随机Kaczmarz算法的性能，以解决$ a x \ of b + \ varepsilon $，其中$ a x = b $是一致的线性系统，$ \ varepsilon $具有独立的零随机条目。我们得出学习率计划，该时间表优化了在某些情况下预期错误的界限；与标准随机Kaczmarz算法的指数收敛相反，我们优化的结合涉及指数的Lambert- $ W $函数的倒数。
We study how the learning rate affects the performance of a relaxed randomized Kaczmarz algorithm for solving $A x \approx b + \varepsilon$, where $A x =b$ is a consistent linear system and $\varepsilon$ has independent mean zero random entries. We derive a learning rate schedule which optimizes a bound on the expected error that is sharp in certain cases; in contrast to the exponential convergence of the standard randomized Kaczmarz algorithm, our optimized bound involves the reciprocal of the Lambert-$W$ function of an exponential.
